Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 1: Functions - Section 1.3 - Trigonometric Functions - Exercises 1.3 - Page 28: 40

Answer

$-\sin{x}$

Work Step by Step

Addition formula $$\sin{(A+B)}= \sin{A} \cos{B} +\cos{A} \sin{B}$$ $\therefore \sin{(2\pi-x)} = \sin{2\pi} \cos{(-x)} + \cos{2\pi} \sin{(-x)}$ $\sin{(2\pi-x)} = (0) \times \cos{x} + (1) \times -\sin{x}$ $\sin{(2\pi-x)} = -\sin{x}$
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.