Q 100. - 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 ${\left[g\left(\theta \right)\right]}^2$.

Step-by-Step Solution

Answer

The value of the function ${\left[g\left(\theta \right)\right]}^2$ is $\frac{1}{4}$.

Step 1. Given information.

Consider the given function ${\left[g\left(\theta \right)\right]}^2$ where $g\left(\theta \right)=\cos \theta$and the value of $\theta =60°$.

Step 2. Finding g θ 2 .

In the trigonometric standard angle the value of $\cos 60°=\frac{1}{2}$.

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

$$\begin{gathered} {\left[g\left(\theta \right)\right]}^2={\left[\cos 60°\right]}^2 \\ ={\left[\frac{1}{2}\right]}^2 \\ =\frac{1}{4} \end{gathered}$$