Question

Use the even–odd properties to find the exact value of each expression. Do not use a calculator.

$\tan (-\mathrm{\pi })$

Short answer

The exact value for the given expression is 0.

Step-by-step solution

Step 1. Given Information

Given that the trigonometric expression is $\tan (-\mathrm{\pi }).$To find the exact value of trigonometric expression using even odd property.

Step 2. Even odd property

Tangent is an odd function and it can be denoted as,

$$\begin{gathered} \tan (-\mathrm{\theta })=-\mathrm{tan\theta } \\ =\frac{-\mathrm{sin\theta }}{\mathrm{cos\theta }} \\ \tan (-\mathrm{\pi })=-\mathrm{tan\pi } \\ =\frac{-\mathrm{sin\pi }}{\mathrm{cos\pi }} \\ =\frac{-0}{-1} \\ \tan (-\mathrm{\pi })=0 \end{gathered}$$