Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix D - Trigonometry - D Exercises - Page A32: 39

Answer

(a) $sin(-\theta)=-sin\theta$ (b) $cos(-\theta)=cos\theta$

Work Step by Step

(a) Need to prove $sin(-\theta)=-sin\theta$ For a right triangle as depicted below $sin\theta=\frac{y}{\sqrt {x^{2}+y^{2}}}$ If we interchange the sign for $\theta$, we will have $sin(-\theta)=-\frac{y}{\sqrt {x^{2}+y^{2}}}$ Hence, $sin(-\theta)=-sin\theta$ (b) (a) Need to prove $cos(-\theta)=cos\theta$ For a right triangle , $cos\theta=\frac{x}{\sqrt {x^{2}+y^{2}}}$ If we interchange the sign for $\theta$, we will have $cos(-\theta)=\frac{x}{\sqrt {x^{2}+y^{2}}}$ Hence, $cos(-\theta)=cos\theta$
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