Question

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

$\sin \left(-\frac{3\mathrm{\pi }}{2}\right)$

Short answer

The exact value for the given expression is -1.

Step-by-step solution

Step 1. Given Information

Given that the trigonometry expression is $\sin \left(-\frac{3\mathrm{\pi }}{2}\right).$To find the exact value of trigonometry expression using even odd function.

Step 2. Even odd property

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

$$\begin{gathered} \sin (-\mathrm{\theta })=-\mathrm{sin\theta } \\ =-\mathrm{y} \\ \sin \left(-\frac{3\mathrm{\pi }}{2}\right)=-\sin \frac{3\mathrm{\pi }}{2} \\ =-\mathrm{y} \\ \sin \left(-\frac{3\mathrm{\pi }}{2}\right)=-1 \end{gathered}$$