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 function cos x = a r = 8 3

Single Variable Calculus: Early Transcendentals, Volume I

8th Edition

ISBN: 9781305270343

Author: James Stewart

Publisher: Cengage Learning

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Chapter D, Problem 60E

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To evaluate: The expression cos(x+y).

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Chapter D Solutions

Single Variable Calculus: Early Transcendentals, Volume I

Ch. D - Prob. 1E Ch. D - Prob. 2E Ch. D - Prob. 3E Ch. D - Prob. 4E Ch. D - Prob. 5E Ch. D - Prob. 6E Ch. D - Prob. 7E Ch. D - Prob. 8E Ch. D - Prob. 9E Ch. D - Prob. 10E

Ch. D - Prob. 11E Ch. D - Prob. 12E Ch. D - Prob. 13E Ch. D - Prob. 14E Ch. D - Prob. 15E Ch. D - Prob. 16E Ch. D - Prob. 17E Ch. D - Prob. 18E Ch. D - Prob. 19E Ch. D - Prob. 20E Ch. D - Prob. 21E Ch. D - Prob. 22E Ch. D - Prob. 23E Ch. D - Prob. 24E Ch. D - Prob. 25E Ch. D - Prob. 26E Ch. D - Prob. 27E Ch. D - Prob. 28E Ch. D - Prob. 29E Ch. D - Prob. 30E Ch. D - Prob. 31E Ch. D - Prob. 32E Ch. D - Prob. 33E Ch. D - Prob. 34E Ch. D - Prob. 35E Ch. D - Prob. 36E Ch. D - Prob. 37E Ch. D - Prob. 38E Ch. D - Prob. 39E Ch. D - Prob. 40E Ch. D - Prob. 41E Ch. D - Prob. 42E Ch. D - Prob. 43E Ch. D - Prob. 44E Ch. D - Prob. 45E Ch. D - Prob. 46E Ch. D - Prob. 47E Ch. D - Prob. 48E Ch. D - Prob. 49E Ch. D - Prob. 50E Ch. D - Prob. 51E Ch. D - Prob. 52E Ch. D - Prob. 53E Ch. D - Prob. 54E Ch. D - Prob. 55E Ch. D - Prob. 56E Ch. D - Prob. 57E Ch. D - Prob. 58E Ch. D - Prob. 59E Ch. D - Prob. 60E Ch. D - Prob. 61E Ch. D - Prob. 62E Ch. D - Prob. 63E Ch. D - Prob. 64E Ch. D - Prob. 65E Ch. D - Prob. 66E Ch. D - Prob. 67E Ch. D - Prob. 68E Ch. D - Find all values of x in the interval [0, 2] that...Ch. D - Prob. 70E Ch. D - Prob. 71E Ch. D - Prob. 72E Ch. D - Prob. 73E Ch. D - Prob. 74E Ch. D - Prob. 75E Ch. D - Prob. 76E Ch. D - Prob. 77E Ch. D - Prob. 78E Ch. D - Prob. 79E Ch. D - Prob. 80E Ch. D - Prob. 81E Ch. D - Prob. 82E Ch. D - Prob. 83E Ch. D - Prob. 84E Ch. D - Prob. 85E Ch. D - Prob. 86E Ch. D - Prob. 87E Ch. D - Prob. 88E Ch. D - Prob. 89E

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The expression cos ( x + y ) .

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To evaluate: The expression cos(x+y).

Chapter D Solutions