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: 34



Work Step by Step

$$X=\sqrt{\frac{1+\cos76^\circ}{2}}$$ Recall the half-angle identity for cosine, which states $$\sqrt{\frac{1+\cos A}{2}}=\cos\frac{A}{2}$$ So we can apply the identity to $X$ with $A=76^\circ$, meaning that $$X=\sqrt{\frac{1+\cos76^\circ}{2}}=\cos\frac{76^\circ}{2}$$ $$X=\cos38^\circ$$ Therefore, $$\sqrt{\frac{1+\cos76^\circ}{2}}=\cos38^\circ$$ $\cos38^\circ$ is a single trigonometric function, so we can stop here.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.