Q. 65 - Precalculus Enhanced with Graphing Utilities

Question

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

$\sin (-{90}^{\mathrm{o}})$

Step-by-Step Solution

Answer

The exact value of trigonometric expression is -1.

Step 1. Given Information

Given that the trigonometric expression is $\sin (-{90}^{\mathrm{o}}).$ To find the exact value of trigonometric expression using even odd property.

Step 2. Even odd property

On applying even odd property,

$$\begin{gathered} \sin (-\mathrm{\theta })=-\sin \left(\mathrm{\theta }\right) \\ \sin (-{90}^{\mathrm{o}})=-\sin \left({90}^{\mathrm{o}}\right) \\ =-\sin (2\times 0+1){90}^{\mathrm{o}} \because \sin (2\mathrm{n}+1){90}^{\mathrm{o}}={(-1)}^{\mathrm{n}} \\ =-{(-1)}^{\mathrm{o}} \\ \sin (-{90}^{\mathrm{o}})=-1 \end{gathered}$$