Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 5 - Trigonometric Identities - Section 5.6 Half-Angle Identities - 5.6 Exercises - Page 242: 32



Work Step by Step

$$\cos x=-0.75\hspace{2cm}\sin x\approx0.6614\hspace{2cm}\tan\frac{x}{2}\approx?$$ According to the half-angle identity for tangents: $$\tan\frac{x}{2}=\frac{\sin x}{1+\cos x}$$ Apply the values of $\cos x$ and $\sin x$ to the formula. $$\tan\frac{x}{2}\approx\frac{0.6614}{1-0.75}$$ $$\tan\frac{x}{2}\approx\frac{0.6614}{0.25}$$ $$\tan\frac{x}{2}\approx2.6456$$
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