Trigonometry (11th Edition) Clone

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

Chapter 5 - Review Exercises - Page 248: 22


$$\cos75^\circ=\sqrt{\frac{1+\cos150^\circ}{2}}$$ 22 goes with C.

Work Step by Step

$$\cos75^\circ$$ We know that $75^\circ=\frac{150^\circ}{2}$ In other words, $75^\circ$ is the half angle of $150^\circ$. Thus, we might apply the half-angle identity here. - The half-angle identity for cosine: $$\cos\frac{\theta}{2}=\pm\sqrt{\frac{1+\cos\theta}{2}}$$ Therefore, $$\cos75^\circ=\pm\sqrt{\frac{1+\cos150^\circ}{2}}$$ $75^\circ$ lies in quadrant I, where cosines are positive. So $\cos75^\circ\gt0$, meaning that $$\cos75^\circ=\sqrt{\frac{1+\cos150^\circ}{2}}$$ That means 22 goes with C.
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