Question

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

$\tan (-{30}^{\mathrm{o}})$

Short answer

The exact value of trigonometric expression is$-\frac{\sqrt{3}}{3}.$

Step-by-step solution

Step 1. Given Information

Given that the trigonometric expression is$\tan (-{30}^{\mathrm{o}})$. To find the exact value of trigonometric expression using even odd property.

Step 2. Even odd property

According to the property of even odd, the function is $\tan (-\mathrm{\theta })=-\mathrm{tan\theta }.$On substituting the value,

$$\begin{gathered} \tan (-{30}^{\mathrm{o}})=-\tan {30}^{\mathrm{o}} \\ \tan {30}^{\mathrm{o}}=\frac{\sqrt{3}}{3} \\ -\tan {30}^{\mathrm{o}}=-\frac{\sqrt{3}}{3} \\ \tan (-{30}^{\mathrm{o}})=-\frac{\sqrt{3}}{3} \end{gathered}$$