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

Short answer

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

Step-by-step solution

Step 1. Given information.

Consider the given function ${\left[g\left(\theta \right)\right]}^2$where localid="1646396871570" $g\left(\theta \right)=\cos \theta$and the value of$\theta =60°$.

Step 2. Finding gθ2.

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

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

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