Q 99. - Precalculus Enhanced with Graphing Utilities

Question

If $f\left(\theta \right)=\sin \theta$ and $g\left(\theta \right)=\cos \theta$. Find the exact value of the function given below if $\theta =60°$. Do not use a calculator.

Function is ${\left[f\left(\theta \right)\right]}^2$.

Step-by-Step Solution

Answer

The value of the function ${\left[f\left(\theta \right)\right]}^2$ is $\frac{3}{4}$.

Step 1. Given information.

Consider the given function $f\left(\theta \right)=\sin \theta$and the value of $\theta =60°$.

Step 2. Finding f θ 2 .

In the trigonometric standard angle the value of $\sin 60°=\frac{\sqrt{3}}{2}$.

Substitute the value in function ${\left[f\left(\theta \right)\right]}^2$.

$$\begin{gathered} {\left[f\left(\theta \right)\right]}^2={\left[\sin 60°\right]}^2 \\ ={\left[\frac{\sqrt{3}}{2}\right]}^2 \\ =\frac{3}{4} \end{gathered}$$