Question

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

$\sin (-\frac{\mathrm{\pi }}{3})$

Short answer

The exact value of trigonometric expression is$-\frac{\sqrt{3}}{2}.$

Step-by-step solution

Step 1. Given Information

Given that the trigonometric expression is $\sin (-\frac{\mathrm{\pi }}{3}).$To find the exact value of expression using even odd property.

Step 2. Even odd property

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

$$\begin{gathered} \sin (-\mathrm{\theta })=-\mathrm{sin\theta } \\ =-\mathrm{y} \\ \sin (-\frac{\mathrm{\pi }}{3})=-\sin \frac{\mathrm{\pi }}{3} \\ =-\mathrm{y} \\ \sin (-\frac{\mathrm{\pi }}{3})=-\frac{\sqrt{3}}{2} \end{gathered}$$