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.

$\tan \left(21\mathrm{\pi }\right)$

Short answer

The exact value is$0.$

Step-by-step solution

Step 1. Given information.

We have:

$\tan \left(21\pi \right)$

Step 2. Find the exact value of trigonometric function.     

The function is $\tan \left(21\pi \right)$.

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the second quadrant.

$$\begin{gathered} =-\tan \left(0\right) \\ =0 \end{gathered}$$