Q. 59 - Precalculus Enhanced with Graphing Utilities

Question

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

$\sin (-{60}^{\mathrm{o}})$

Step-by-Step Solution

Answer

The value can be found as $-\frac{\sqrt{3}}{2}.$

Step 1. Given Information

Given that the expression is $\sin (-{60}^{\mathrm{o}}).$ To find the value of expression using Even odd property.

Step 2. Even Odd property

The property of even odd property is $\sin (-\mathrm{\theta })=-\mathrm{sin\theta }.$ On substituting the value,

$$\begin{gathered} \sin (-{60}^{\mathrm{o}})=-\sin {60}^{\mathrm{o}} \\ \sin {60}^{\mathrm{o}}=\frac{\sqrt{3}}{2} \\ -\sin {60}^{\mathrm{o}}=-\frac{\sqrt{3}}{2} \\ \sin (-{60}^{\mathrm{o}})=-\frac{\sqrt{3}}{2} \end{gathered}$$