Q 98. - 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 calculator.

Function is $g\left(\frac{\theta }{2}\right)$.

Step-by-Step Solution

Answer

The value of $g\left(\frac{\theta }{2}\right)$ is $\frac{\sqrt{3}}{2}$.

Step 1. Given information.

Consider the given function $g\left(\frac{\theta }{2}\right)$and the value of $\theta =60°$.

Step 2. Finding g θ 2 .

In the trigonometric standard angles the value of $\cos 30°=\frac{\sqrt{3}}{2}$.

Substitute the value in $g\left(\frac{\theta }{2}\right)$.

$$\begin{gathered} g\left(\frac{\theta }{2}\right)=g\left(\frac{60°}{2}\right) \\ g\left(\frac{\theta }{2}\right)=g\left(30°\right) \end{gathered}$$

Further simplify.

$$\begin{gathered} g\left(30°\right)=\cos 30° \\ =\frac{\sqrt{3}}{2} \end{gathered}$$