Trigonometry (11th Edition) Clone

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

Chapter 4 - Test - Page 193: 3c



Work Step by Step

The tangent function is the sine function divided by the cosine function. Therefore, we need to find a value in which cosine is 0 in order to get an undefined tangent. Now, the cosine graph passes 0 at $\frac{\pi}{2}$ and $\frac{3\pi}{2}$. Therefore, the least positive value for which cosine is 0 is $\frac{\pi}{2}$. This means that tan$\frac{\pi}{2}$ can be written as sin $\frac{\pi}{2}$ divided by cos $\frac{\pi}{2}$. Since sin $\frac{\pi}{2}$ is 1 and cos $\frac{\pi}{2}$ is zero, this means that tan$\frac{\pi}{2}$ is $1/0$ which is undefined. Therefore, the least positive value for which the tangent function is undefined is $\frac{\pi}{2}$.
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