Explanation Result used: “Let P ( a , b ) be any point on the terminal side of angle θ and let r be the distance between the points P ( a , b ) and ( 0 , 0 ) then, sin θ = b r , csc θ = r b , cos θ = a r , sec θ = r a , tan θ = b a and cot θ = a b .” Calculation: It is given that sin x = 1 3 and sec y = 5 4 . From the above result, the trigonometric function sin θ = b r . That is, b r = 1 3 . Here, acute angle x belongs to the first quadrant. Thus, the value of a and b are positive. Therefore, the value of b = 1 and r = 3 . Use the Pythagorean Theorem ( hyp ) 2 = ( adj ) 2 + ( opp ) 2 , to obtain the value of a. a = r 2 − b 2 = 3 2 − 1 2 = 9 − 1 = ± 8 Thus, the value of a is 8 . Therefore, the trigonometric ratio cos x = a r = 8 3

Essential Calculus: Early Transcendentals

2nd Edition

ISBN: 9781133112280

Author: James Stewart

Publisher: Cengage Learning

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Chapter A, Problem 59E

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Chapter A, Problem 58E

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Chapter A Solutions

Essential Calculus: Early Transcendentals

Ch. A - Prob. 1E Ch. A - Convert from degrees to radians. 300 Ch. A - Convert from degrees to radians. 9 Ch. A - Convert from degrees to radians. 315 Ch. A - Convert from degrees to radians. 900 Ch. A - Convert from degrees to radians. 36 Ch. A - Convert from radians to degrees. 4 Ch. A - Convert from radians to degrees. 72 Ch. A - Convert from radians to degrees. 512 Ch. A - Convert from radians to degrees. 83

Ch. A - Convert from radians to degrees. 38 Ch. A - Convert from radians to degrees. 5 Ch. A - Find the length of a circular arc subtended by an...Ch. A - If a circle has radius 10 cm, find the length of...Ch. A - A circle has radius 1.5 m. What angle is subtended...Ch. A - Find the radius of a circular sector with angle...Ch. A - Draw, in standard position, the angle whose...Ch. A - Draw, in standard position, the angle whose...Ch. A - Draw, in standard position, the angle whose...Ch. A - Draw, in standard position, the angle whose...Ch. A - Draw, in standard position, the angle whose...Ch. A - Draw, in standard position, the angle whose...Ch. A - Find the exact trigonometric ratios for the angle...Ch. A - Find the exact trigonometric ratios for the angle...Ch. A - Find the exact trigonometric ratios for the angle...Ch. A - Find the exact trigonometric ratios for the angle...Ch. A - Find the exact trigonometric ratios for the angle...Ch. A - Find the exact trigonometric ratios for the angle...Ch. A - Find the remaining trigonometric ratios. sin=35,02 Ch. A - Find the remaining trigonometric ratios. tan=2,02 Ch. A - Find the remaining trigonometric ratios. sec=1.5,2 Ch. A - Find the remaining trigonometric ratios....Ch. A - Find the remaining trigonometric ratios. cot=3,2 Ch. A - Find the remaining trigonometric ratios....Ch. A - Find, correct to five decimal places, the length...Ch. A - Find, correct to five decimal places, the length...Ch. A - Find, correct to five decimal places, the length...Ch. A - Find, correct to five decimal places, the length...Ch. A - Prove each equation. (a) Equation 10a (b) Equation...Ch. A - Prove each equation. (a) Equation 14a (b) Equation...Ch. A - Prove each equation. (a) Equation 18a (b) Equation...Ch. A - Prove the identity. cos(2x)=sinx Ch. A - Prove the identity. sin(2+x)=cosx Ch. A - Prove the identity. sin(x)=sinx Ch. A - Prove the identity. sincot=cos Ch. A - Prove the identity. (sinx+cosx)2=1+sin2x Ch. A - Prove the identity. secycosy=tanysiny Ch. A - Prove the identity. tan2sin2=tan2sin2 Ch. A - Prove the identity. cot2+sec2=tan2+csc2 Ch. A - Prove the identity. 2csc2t=sectcsct Ch. A - Prob. 51E Ch. A - Prob. 52E Ch. A - Prob. 53E Ch. A - Prob. 54E Ch. A - Prob. 55E Ch. A - Prob. 56E Ch. A - Prob. 57E Ch. A - Prob. 58E Ch. A - Prob. 59E Ch. A - Prob. 60E Ch. A - Prob. 61E Ch. A - Prob. 62E Ch. A - Prob. 63E Ch. A - Prob. 64E Ch. A - Prob. 65E Ch. A - Prob. 66E Ch. A - Prob. 67E Ch. A - Prob. 68E Ch. A - Prob. 69E Ch. A - Prob. 70E Ch. A - Prob. 71E Ch. A - Prob. 72E Ch. A - Prob. 73E Ch. A - Prob. 74E Ch. A - Prob. 75E Ch. A - Prob. 76E Ch. A - Prob. 77E Ch. A - Prob. 78E Ch. A - Prob. 79E Ch. A - Prob. 80E Ch. A - Prob. 81E Ch. A - Prob. 82E Ch. A - Prob. 83E Ch. A - Prob. 84E Ch. A - Prob. 85E Ch. A - Prob. 86E Ch. A - Prob. 87E Ch. A - Prob. 88E Ch. A - Find the area of triangle ABC, correct to five...

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The expression sin ( x + y ) .

Solution Summary: The author evaluates the expression mathrmsin(x+y) using the Pythagorean Theorem.

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Chapter A Solutions