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.

$\tan 405°$

Short answer

The exact value is$1$.

Step-by-step solution

Step 1. Given information.

We have:

$\tan \left({405}^{\circ \hspace{0.17em}}\right)$

Step 2. Find the exact value of trigonometric function.  

The function is $\tan \left({405}^{\circ \hspace{0.17em}}\right)$.

Formula used:

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

Remove full rotations of $360°$until the angle is between $0°$to $360°$

We get:

$$\begin{gathered} \tan \left({405}^{\circ \hspace{0.17em}}\right)=\tan 45° \\ =1 \end{gathered}$$