Q. 18 - Precalculus Enhanced with Graphing Utilities

Question

If f(x)=sin x  and f(a)=$\frac{3}{5}$ , find f(-a)

Step-by-Step Solution

Answer

f(-a)=$\frac{-3}{5}$

Step 1. Given information

f(x)=sin x 

f(a) = $\frac{3}{5}$

Step 2. Solving for a

Given $$\begin{gathered} f\left(a\right)=\frac{3}{5} \\ \Rightarrow a = 37° \end{gathered}$$

Step 3. Solving of f(-a)

$$\begin{gathered} f(-a)=f(-37°)=\sin (-37°) \\ \left\{\sin \right(-x)=-\sin x\} \\ \Rightarrow f(-a)=\frac{-3}{5} \end{gathered}$$