Answer
$T=2\pi$
Work Step by Step
For a function of the form $\sin{(ax+b)}$, the period $(T)$ is given by:
$$T=\dfrac{2\pi}{a}$$
For $\sin{\left(x+\dfrac{\pi}{6}\right)}$, $a=1$
$T=\dfrac{2\pi}{1} = 2\pi$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
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 27: 20
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