Q. 25 - Precalculus Enhanced with Graphing Utilities

Question

In problems 11-26, use the fact that the trigonometric function are periodic to find the exact value of each expression. Do not use a calculator.

$\tan \left(\frac{19\pi }{6}\right)$

Step-by-Step Solution

Answer

The exact value is $\frac{\sqrt{3}}{3}$.

Step 1. Given information.

We have:

$\tan \left(\frac{19\pi }{6}\right)$

Step 2. Find the exact value of trigonometric function.

The function is $\tan \left(\frac{19\pi }{6}\right)$.

Formula used:

$\tan \left(\theta +\pi \right)=\tan \theta$

$$\begin{gathered} =\tan \left(\frac{\pi }{6}\right) \\ =\frac{\sqrt{3}}{3} \end{gathered}$$