Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 7 - P.S. Problem Solving - Page 557: 2



Work Step by Step

Our aim is to prove that $\theta=\dfrac{(2n+1)\pi}{2}$ Let us suppose that $\theta$ is an angle such that $\cos \theta =0$. Recall that any odd multiple of $\dfrac{\pi}{2}$ satisfies the equation $\cos \theta =0$. This implies that $\theta=(a)(\dfrac{\pi}{2})$ for any odd integer $a$ would also satisfy the equation $\cos \theta =0$. So, we can write this as: $\theta=(a)(\dfrac{\pi}{2}) \implies \theta=(2n+1)(\dfrac{\pi}{2})$ Thus the result has been proven: $\theta=\dfrac{(2n+1)\pi}{2}$
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