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

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ISBN: 9781337772020

Author: Stewart

Publisher: VST

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Chapter A, Problem 60E

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Chapter A, Problem 59E

Chapter A, Problem 61E

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Chapter A Solutions

EBK WEBASSIGN FOR STEWART'S ESSENTIAL C

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

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The expression cos ( x + y ) .

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

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Chapter A Solutions