Q. 17 - 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.

$\cot \left({390}^{\circ \hspace{0.17em}}\right)$

Step-by-Step Solution

Answer

The exact value is $\sqrt{3}$.

Step 1. Given information.

We have:

$\cot \left({390}^{\circ \hspace{0.17em}}\right)$

Step 2. Find the exact value of trigonometric function.

The function is $\cot \left({390}^{\circ \hspace{0.17em}}\right)$.

Formula used:

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

Remove full rotation of $360°$ until the angle between $0°$ to $360°$.

We get:

$$\begin{gathered} \cot \left({390}^{\circ \hspace{0.17em}}\right)=\cot \left({30}^{\circ \hspace{0.17em}}\right) \\ =\sqrt{3} \end{gathered}$$