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 27: 16



Work Step by Step

When we are presented with a function such as $sin(bx)$ and are asked to find the period, it is useful to make use of the following formula: $\frac{2\pi}{T}=b$ The $T$ in the equation represents the period of the function, as in the amount of $x$ units before the function repeats itself. In this question, we have $cos(\frac{\pi x}{2})$. Thus, $\frac{2\pi}{\frac{\pi}{2}}=T=4$ . Keep in mind that the formula above allows us to easily swap the $T$ and the $b$ in the formula, thus, the period of this function is $4$.
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