Algebra and Trigonometry (5th Edition)

Chapter 6

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;;; ; ; ; Substitute 15 for opp, and 17 for hyp ... more

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; ;; ; ; ; Substitute for opp and for hyp into ... more

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;; ; ; ; ; Substitute for opp and 6 for hyp into ... more

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;; ; ; ; ; Substitute 16 for opp and for hyp into... more

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; ; ;; ; ; Substitute 27 for a and 14 for b into ... more

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; ; ; ; ; ; Substitute for band 9 for c into the ... more

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; ; ; Substitute for into the reciprocal function ... more

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; ;  ; Substitute for into the reciprocal ... more

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;; ; ; ; Draw a right angle triangle with the side... more

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;; ; ; ; Draw a right angle triangle with the ... more

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; ; ; ; ; Draw a right angle triangle with the ... more

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; ; ; ; ; Draw a right angle triangle with the ... more

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; ; ; ; ; Draw a right angle triangle with the ... more

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; ; ; ; ; Draw a right angle triangle with the ... more

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; ; ; ; ; Draw a right angle triangle with the ... more

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; ; ; ; ; Draw a right angle triangle with the ... more

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; Draw an isosceles right angle triangle with the... more

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; Draw an equilateral triangle with sides of ... more

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; Draw an equilateral triangle with sides of ... more

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; Draw an isosceles right angle triangle with the... more

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; Draw an equilateral triangle with sides of ... more

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; Draw an isosceles right angled triangle with ... more

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; Draw an equilateral triangle withthe length of ... more

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; Draw an equilateral triangle with the side of ... more

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1 ; Draw an isosceles right-angled triangle with ... more

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; Draw an equilateral triangle with the length of... more

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2 ; Draw an equilateral triangle with the length ... more

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; Draw an equilateral triangle with the length of... more

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ft ; The length of adjacent and opposite sides of... more

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ft ; The length of the adjacent side toangle can... more

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; Set the calculator to DEGREE mode and enter the... more

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; Set the calculator to DEGREE mode and enter the... more

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; Set the calculator to DEGREE mode and enter the... more

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; Set the calculator to DEGREE mode and enter the... more

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; Set the calculator to DEGREE mode and enter the... more

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; Set the calculator to DEGREE mode and enter the... more

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; Set the calculator to DEGREE mode and enter the... more

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; Set the calculator to DEGREE mode and enter the... more

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; Set the calculator to DEGREE mode and enter the... more

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; Set the calculator to DEGREE mode and enter the... more

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; Set the calculator to DEGREE mode and enter the... more

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; Set the calculator to DEGREE mode and enter the... more

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; Set the calculator to DMS feature and enter the... more

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; Set the calculator to DMS feature and enter the... more

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; Set the calculator to DMS feature and enter the... more

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; Set the calculator to DMS feature and enter the... more

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; Set the calculator to the DMS feature and enter... more

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; Set the calculator to the DMS feature and enter... more

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; Set the calculator to the DMS feature and enter... more

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; Set the calculator to the DMS feature and enter... more

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; Write the given expression as a sum of and... more

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; Write the given expression as a sum of and . ; ... more

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; Write the given expression as a sum of and . ; ... more

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; Write the given expression as a sum of and . ; ... more

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; Set the calculator in DEGREE mode and obtain ... more

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; Write the given function in terms of tangent ... more

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; Set the calculator in DEGREE mode and obtain ... more

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; Set the calculator in DEGREE mode and obtain ... more

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; Write the given function in terms of cosine ... more

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; Set the calculator in DEGREE mode and obtain ... more

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; Set the calculator in DEGREE mode and obtain ... more

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; Write the given function in terms of sine ... more

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; Set the calculator in DEGREE mode and obtain ... more

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; Set the calculator in DEGREE mode and obtain ... more

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; Set the calculator in DEGREE mode and obtain ... more

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; Set the calculator in DEGREE mode and obtain ... more

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; Write the given function in terms of sine ... more

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; Write the given function in terms of cosine ... more

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; Write the given function in terms of tangent ... more

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; Set the calculator in DEGREE mode and obtain ... more

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; Set the calculator in DEGREE mode.Use the ... more

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; Set the calculator in DEGREE mode. Use the ... more

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; Set the calculator in DEGREE mode.  Use the ... more

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; Set the calculator in DEGREE mode.Use the ... more

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; Set the calculator in DEGREE mode. Use the ... more

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; Set the calculator in DEGREE mode. Use the ... more

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; Set the calculator in DEGREE mode.Use the ... more

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; Set the calculator in DEGREE mode. Use the ... more

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; Simplify the reciprocal function for . ; ... more

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; Simplify the reciprocal function for. ; ... more

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; Simplify the reciprocal function for. ; ... more

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; Simplify the reciprocal function for. ; ... more

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         ; Simplify the right side of the given ... more

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; Use the reciprocal function, , to write the ... more

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; Simplify the right side of the given equation ... more

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; Simplify the right side of the given equation ... more

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; Use CAS in DEGREE mode to find the exact value ... more

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; Simplify the right side of the given equation ... more

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; Use the reciprocal function, , to write the ... more

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; Express the given tangent function as a decimal... more

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; Use the reciprocal function, , to write the ... more

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; Use the reciprocal function, , to write the ... more

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; Substitute for into the cofunction identity ... more

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; Substitute for into the cofunction identity ... more

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; Substitute for into the cofunction identity ... more

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; Substitute for into the cofunction identity ... more

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; Substitute for into the cofunction identity ... more

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; Substitute for into the cofunction identity ... more

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; Substitute for into the cofunction identity ... more

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; Substitute for into the cofunction identity ... more

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; Substitute for into the cofunction identity ... more

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Replace with y. This implies that .Substitute ... more

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Replace with y. This implies that .Substitute ... more

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Write the given equation in the exponential form... more

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Replace byinto the given equation. ; Substitute ... more

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; Apply natural log on both the sides of the ... more

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4 ; Write 625 as in the given equation.Apply log ... more

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; Apply the quotient rule on the left side of the... more

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343 ; Write the given equation in exponential form... more

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; The cofunction identity of secant function is .... more

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; The cofunction identity of secant function is .... more

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; Substitute for b and q for c into the ... more

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Entire Proof Answer:   ; Let the height of the ... more

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; As the measure of is , this implies that the ... more

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; As the measure ofis , this implies that the sum... more

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; As the measure of is , this implies that the ... more

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; As the measure of is , this implies that the ... more

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; As the measure of is , this implies that the ... more

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; As the measure of is , this implies that the ... more

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; As the measure of C is , this implies that the ... more

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; Substitute for , for opp, and for adj into ... more

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; Substitute for , 100 for adj, and 450 for hyp ... more

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; As the measure of C is , this implies that the ... more

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; As the measure of C is , this implies that the ... more

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; As the measure of C is , this implies that the ... more

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; As the measure of C is , this implies that the ... more

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; As the measure of C is , this implies that the ... more

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; Substitute for , for adj, and for hyp into ... more

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; Substitute for , for opp, and for hyp into ... more

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; Alternate interior angles are equal when a ... more

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inches ; Each acute angle of an isosceles triangle... more

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; Plot the triangle. ; Substitute 1320 for ... more

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 61 ft ; Substitute for hypotenuse, 50 for ... more

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12 ft 10 inch  ; Multiply the length in feet by 12... more

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81 inches ; Plot the triangle. ; Substitute for ... more

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; Sketch the triangle. ; Substitute for opposite... more

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324 ft ; Substitute for opposite side, 135 for ... more

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424 ft ; Sketch the triangles. ; Substitute for ... more

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750 ft ; Sketch the triangles. ; Substitute for ... more

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cm ; Draw a diagram for the given problem.Assume a... more

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miles ; Sketch the triangles. ; Substitute for ... more

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45 ft ; Sketch the triangles. ; Apply tangent ... more

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45 ft ; Sketch the triangles. ; Apply tangent ... more

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Radius: in; length: in; width:in. ; Draw a diagram... more

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ft ; Sketch the triangle. ; Equate with the pitch... more

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ft ; Sketch the triangle. ; Equate to the pitch ... more

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; Sketch the triangle. ; The angle of elevation ... more

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8 km ; Sketch the triangles. ; Use tangent ... more

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275 ft ; Sketch the triangle. ; The property of ... more

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miles ; Sketch the triangle. ; The property of ... more

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23 ft ; Sketch the triangles. ; Use the tangent ... more

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24 km ; Sketch the triangle. ; Apply angle sum ... more

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; Substitute for , 0 for , for, and 0 for ... more

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; Substitute for, for , for  , and for  into ... more

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; Take natural logarithms on the both sides. ; 4 ... more

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; The exponential equation, , is equivalent to ... more

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cm ; Sketch the triangle. ; Substitute for, for ... more

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; Draw a diagram for the given problem. ; Use the... more

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Quadrant III ; To represent the given angle, fix ... more

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Quadrant IV ; To represent the given angle, fix ... more

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Quadrant III ; 1 degree is equal to 60 minutes, so... more

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Quadrant III ; To represent the given angle, fix ... more

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Quadrant I ; To represent the given angle, fix the... more

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Quadrant IV ; To represent the given angle, fix ... more

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Quadrant III ; To represent the given angle, fix ... more

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Quadrant IV ; To represent the given angle, fix ... more

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Quadrant II ; To represent the given angle, fix ... more

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I quadrant ; Since 1 degree is equal to 60 minutes... more

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II Quadrant ; To represent the given angle, fix ... more

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I quadrant ; To represent the given angle, fix ... more

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, , ; To find the first positive angle, add to the... more

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, , ; To find the first positive angle, add to ... more

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, , ; To find the first positive angle, add to ... more

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, , ; To find the first positive angle, add to ... more

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, , ; To find the first positive angle, add to ... more

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, , ; To find the first positive angle, add to ... more

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Complement: Supplement: ; To find the complement ... more

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·         Complement: ·         Supplement: ; To ... more

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Complement: Supplement: ; To find the complement ... more

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Complement: Supplement: ; To find the complement ... more

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Complement: Supplement: ; To find the complement ... more

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Complement: Supplement: ; To find the complement ... more

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; To evaluate the distance from the origin to the... more

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; To evaluate the distance from the origin to the... more

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; To evaluate the distance from the origin to the... more

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; To evaluate the distance from the origin to the... more

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; To evaluate the distance from the origin to the... more

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; To evaluate the distance from the origin to the... more

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; To determine a point in the IV quadrant, ... more

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; To determine a point in the II quadrant, ... more

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; To determine a point in the I quadrant, ... more

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; To determine a point in the III quadrant, ... more

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  ; Since  is in III quadrant, write  as . ; ... more

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  ; Since  is in I quadrant, write 5 as ; ... more

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  ; Since  is in IV quadrant, write  as . ; ... more

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; Since  is in II quadrant, write  as . ; ... more

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; Substitute 3 for  and 5 for  into the equation... more

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; Since  is in III quadrant, write  as . ; ... more

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; The terminal side of the given angle lies in ... more

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; Evaluate the co terminal angle by adding to ... more

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1 ; Evaluate the co terminal angle by adding to ... more

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; The reference angle for is the acute angle ... more

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0 ; Evaluate the coterminal angle by subtracting ... more

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Not definedNot defined ; Since the difference ... more

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; Evaluate the coterminal angle by subtracting ... more

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  ; Evaluate the coterminal angle by subtracting ... more

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2 ; Evaluate the coterminal angle by adding to ... more

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  ; Evaluate the coterminal angle for the given ... more

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; Evaluate the coterminal angle by ... more

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; Evaluate the coterminal angle by adding to the... more

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; Evaluate the coterminal angle by subtracting ... more

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  ; Evaluate the coterminal angle by subtracting ... more

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Not definedNot defined ; The difference between ... more

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Not defined1 ; Since the difference between the ... more

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Not defined ; Since the difference between the ... more

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Not defined1 ; Since the difference between the ... more

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;  The terminal side of the given angle lies in ... more

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Not definedNot defined ; The angle difference ... more

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; Evaluate the coterminal angle for the given ... more

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; Evaluate the coterminal angle for the given ... more

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; The terminal side of the given angle lies in ... more

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Not defined ; Evaluate the coterminal angle for ... more

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Not defined1 ; The difference between the given ... more

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; Evaluate the coterminal angle for the given ... more

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Not defined0 ; The difference between the given ... more

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  ; Evaluate the coterminal angle for the given ... more

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Not defined0 ; The difference between the given ... more

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; Evaluate the coterminal angle for the given ... more

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 Not defined0 ;   The difference between the given... more

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Not defined0 ; The angle between the given angle ... more

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Positive: cosine and secantNegative: sine, ... more

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 Positive: cosine and secantNegative: sine, ... more

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Positive: tangent and cotangentNegative: sine, ... more

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Positive: sine and cosecantNegative: tangent, ... more

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Positive: sine and cosecantNegative: tangent, ... more

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Positive: cosine and secantNegative: sine, ... more

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Positive: sine, cosecant, tangent, cotangent, ... more

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Positive: sine and cosecantNegative: tangent, ... more

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; Evaluate the co-terminal angle by subtracting ... more

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; Evaluate the co-terminal angle by subtracting ... more

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; Evaluate the co-terminal angle by subtracting ... more

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; Evaluate the co-terminal angle with the given ... more

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; Fix the CAS in DEGREE mode.Enter the given ... more

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; Fix the CAS in DEGREE mode.Enter the given ... more

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; Write the given function in terms of tangent ... more

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; Fix the CAS in DEGREE mode.Enter the given ... more

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; Fix the CAS in DEGREE mode.Enter the given ... more

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; Fix the CAS in DEGREE mode.Enter the given ... more

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; Fix the CAS in DEGREE mode.Enter the given ... more

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; Fix the CAS in DEGREE mode.Enter the given ... more

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; Fix the CAS in DEGREE mode.Enter the given ... more

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; Write the given function in terms of cosine ... more

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; Write the given function in terms of cosine ... more

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; Fix the CAS in DEGREE mode.Enter the given ... more

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; For the given interval, sketch the angle  in ... more

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; For the given interval, sketch the angle  in ... more

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; For the given interval, sketch the angle  in ... more

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; For the given interval, sketch the angle  in ... more

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; For the given interval, sketch angle  in the ... more

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; For the given interval, sketch angle  in the ... more

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; For the given interval, sketch angle  in the ... more

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; For the given interval, sketch angle  in the ... more

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East: 130 kmSouth: 75 km ; Plot a graphical ... more

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West: about 87 mi; North: 50 mi ; Let the distance... more

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About 223 km ; Substitute 150 for , 2 for  into ... more

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About 181 km ; Substitute 120 for , 2 for  into ... more

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Factor the denominator of the given function using... more

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The degree of the leading term in the given ... more

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Domain: ; Range:  ; Equate the denominator of the ... more

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Domain: ; Range: all real numbers ; Equate the ... more

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12 ; Equate the given function to 0.Add  to both ... more

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, 3 ; Equate the given function to 0. ; The ... more

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; Equate the given function to 0.Add  to both ... more

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, ; Equate the given function to 0. ; The obtained... more

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About feet ; Divide the distance of centre of ... more

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; Make the reference diagram according to the ... more

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The values of all trigonometric functions are ... more

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Sketch a diagram of two right triangles having ... more

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Substitute for into the given trigonometric ... more

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; ; ; As the measure of R is , this implies that ... more

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, , ; Substitute B for , for adj, and for hyp ... more

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, ; , ; For any angle , the set of all coterminal ... more

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, ; , ; For any angle , the set of all coterminal ... more

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; ; Subtract from to find the complement of the ... more

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; ; Subtract from to find the complement of the ... more

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; Plot a diagram which represents the terminal ... more

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; Find the distance  from the origin  to the ... more

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; The value of  is defined as the ratio of -... more

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;;;; ; As cosine function is defined as ratio of ... more

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; Write the given expression in expanded form... more

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; Write the given expression in expanded form... more

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; ; ; ; ; ; Find , using the reciprocal function... more

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; Set the MODE to degrees into the CAS.Press 2nd ... more

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About 290 mi ; Substitute 200 for ,  for  into the... more

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; Plot a diagram that represents the terminal ... more

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; Make a right triangle having the acute angles ... more

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; Draw an equilateral triangle with sides of ... more

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; Plot a diagram that represents the terminal ... more

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; Draw a right triangle having the acute angles ... more

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; Draw a diagram which represents the terminal ... more

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1 ; Draw an angle of and label a point,, on the ... more

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0 ; Draw an angle of and label a point,, on the ... more

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; Plot a diagram that represents the terminal ... more

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; Draw an angle of and label a point,, on the ... more

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;  Draw a diagram which represents the terminal ... more

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1 ; Plot a diagram which represents the terminal ... more

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; Plot a diagram which represents the terminal ... more

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; Draw a right triangle having the acute angles ... more

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; Draw a diagram which represents the terminal ... more

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Not defined ; Make an angle of and label a point... more

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2 ;  Draw a diagram which represents the terminal ... more

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Not defined ; Draw an angle of and label a point... more

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1 ; Make an angle of and label a point on the ... more

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; Draw the diagram which represents the terminal ... more

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; Set the MODE to degree in CAS.Enter the given ... more

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; Apply the reciprocal function formula, , to the... more

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; Set the MODE to degree in CAS.Enter the given ... more

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; Set the MODE to degree in CAS.Enter the given ... more

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; Apply the reciprocal function formula, , to the... more

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; Apply the reciprocal function formula, , to the... more

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; Set the MODE to degree in CAS.Enter the given ... more

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; Set the MODE to degree in CAS. Enter the given ... more

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For different points on the radius line, the value... more

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If  and are reciprocal functions, then .If  and ... more

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Sine:  Cosine: Tangent: ;  The values of sine ... more

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As , the domain for and is all values of . At , ... more

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Since is a positive real number, move the point ... more

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Since is a positive real number, move the point ... more

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Since is a positive real number, move the point ... more

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Since is a negative real number, move the point ... more

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; ; ; ; Draw a unit circle with commonly used ... more

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; ; ; ; Draw a unit circle with commonly used ... more

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Multiply by to convert it into degrees.Since is... more

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Multiply by to convert it into degrees.Since is... more

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; Multiply the given angle by . ; Simplify the ... more

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; Multiply the given angle by . ; Simplify the ... more

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; Multiply the given angle by . ; Simplify the ... more

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; Multiply the given angle by . ; Simplify the ... more

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; Multiply the given angle by . ; more

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; Multiply the given angle by . ; more

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; Multiply the given angle by . ; Simplify the ... more

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; Multiply the given angle by . ; Simplify the ... more

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; Multiply the angle value by . ; Simplify the ... more

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; Multiply the given angle by . ; more

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; Multiply the given angle by . ; Simplify the ... more

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; Multiply the given angle by . ; Simplify the ... more

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; Multiply the given angle by . ; Substitute for... more

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; Multiply the given angle by . ; Substitute for... more

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; Multiply the given value by . ; Substitute for... more

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; Multiply the given angle by . ; Substitute for... more

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; Multiply the given angle by . ; Substitute for... more

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; Multiply the given angle by . ; Substitute for... more

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; Multiply the given angle by . ; Substitute 3.14... more

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; Multiply the given angle by .  ; Substitute 3.... more

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; Multiply the given angle by . ; Substitute 3.14... more

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; Multiply the given angle by . ; Substitute 3.14... more

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; Multiply the given angle by . ; Substitute 3.14... more

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; Multiply the given angle by . ; Substitute 3.14... more

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; Multiply the given angle in radian by . ; ... more

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; Multiply the given angle in radian by . ; ... more

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; Multiply the given angle in radian by . ; ... more

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; Multiply the given angle in radian by . ; ... more

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; Multiply the given angle in radian by to ... more

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; Multiply the given angle in radian by . ; ... more

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; Multiply the given angle in radian by. ; ... more

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; Multiply the given angle in radian by . ; ... more

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; Multiply the given angle in radian by . ; ... more

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; Multiply the given angle in radian by . ; ... more

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; Multiply the given angle by . ; Substitute 3.... more

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; Multiply the given angle by . ; Substitute 3.... more

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; Multiply the given angle in radian by. ; ... more

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; Multiply the given angle in radian by. ; ... more

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, , , , , ,, , , , ; Multiply by . ; Multiply ... more

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, , , , , , , , , , ; Multiply by to convert it ... more

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; Add to the given angle to find the positive ... more

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; Add to the given angle to find the positive ... more

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; Add to the given angle to find the positive ... more

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; Add to the given angle to find the positive ... more

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; Add to the given angle to find the positive ... more

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; Add to the given angle to find the positive ... more

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Complement: ; Supplement: ; Since in radian is ... more

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Complement: ; Supplement: ; Since in radian is ... more

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Complement: ; Supplement: ; Since in radian is ... more

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