Explanation Given information: t = 5 π , − 2 π , 17 π 2 , − 13 π 2 . Formula used: Properties of sin t sin ( t ± 2 π ) = sin t sin ( − t ) = − sin t Calculation: t = 5 π , it can be rewritten as t = 5 π = 2 π + 3 π . ⇒ sin ( 5 π ) = sin ( 2 π + 3 π ) And applying the property sin ( t ± 2 π ) = sin t , ⇒ sin ( 5 π ) = sin ( 2 π + 3 π ) = sin 3 π Similarly, 3 π = 2 π + π ⇒ sin ( 3 π ) = sin ( 2 π + π ) And applying the property sin ( t ± 2 π ) = sin t , sin ( 3 π ) = sin ( 2 π + π ) = sin π = 0 . Now, t = − 2 π can be rewritten as, t = − 2 π = 0 − 2 π ⇒ sin ( − 2 π ) = sin ( 0 − 2 π ) And applying the property sin ( t ± 2 π ) = sin t sin ( − 2 π ) = sin ( 0 − 2 π ) = sin 0 = 0 . t = 17 π 2 can be rewritten as t = 17 π 2 = 2 π + 13 π 2 ⇒ sin ( 17 π 2 ) = sin ( 2 π + 13 π 2 ) And applying the property sin ( t ± 2 π ) = sin t , sin ( 17 π 2 ) = sin ( 2 π + 13 π 2 ) = sin ( 13 π 2 ) Also, 13 π 2 = 2 π + 9 π 2 ⇒ sin ( 13 π 2 ) = sin ( 2 π + 9 π 2 ) And applying the property sin ( t ± 2 π ) = sin t ⇒ sin ( 13 π 2 )

12th Edition

ISBN: 9780137590810

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

Publisher: PEARSON

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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 37E

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To calculate: The value of sint for t=5π, −2π, 17π 2, −13π 2

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Chapter 8.2, Problem 36E

Chapter 8.2, Problem 38E

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The value of sin t for t = 5 π , − 2 π , 17 π 2 , − 13 π 2

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