Explanation Given information: sin ( 0.42 ) = 0.41 Formula Used: Properties of sin t and cos t sin 2 t + cos 2 t = 1 sin ( t + 2 π ) = sin t sin ( − t ) = − sin t Calculation: By using sin ( − t ) = − sin t , sin ( − 0.42 ) = − sin ( 0.42 ) = 0.41 Now, for sin ( 6 π − 0.42 ) = sin ( 2 π + 4 π − 0.42 ) Using sin ( t + 2 π ) = sin t ⇒ sin ( 6 π − 0.42 ) = sin ( 2 π + 4 π − 0.42 ) = sin ( 4 π − 0.42 ) ⇒ sin ( 6 π − 0.42 ) = sin ( 4 π − 0.42 ) = sin ( 2 π + 2 π − 0.42 ) = sin ( 2 π − 0.42 ) ⇒ sin ( 6 π − 0

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ISBN: 9780137590896

Author: Larry J. Goldstein; David C. Lay; David I. Schneider; Nakhle H. Asmar; William Edward Tavernetti

Publisher: Pearson Education (US)

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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Chapter 8.2, Problem 40E

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To calculate: The value of sin(−0.42), sin(6π−0.42), cos(0.42) using properties of cosine and sine and assuming the value of sin(0.42)=0.41.

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Chapter 8.2, Problem 39E

Chapter 8.2, Problem 41E

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The value of sin ( − 0.42 ) , sin ( 6 π − 0.42 ) , cos ( 0.42 ) using properties of cosine and sine and assuming the value of sin ( 0.42 ) = 0.41 .

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To calculate: The value of sin(−0.42), sin(6π−0.42), cos(0.42) using properties of cosine and sine and assuming the value of sin(0.42)=0.41.

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Chapter 8 Solutions