Q 97. - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

The value of $f\left(\frac{\theta }{2}\right)$ is $\frac{1}{2}$.

Step 1. Given information.

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

Step 2. Finding f θ 2 .

In trigonometric standard angles the value of $\sin 30°=\frac{1}{2}$.

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

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

Further simplify.

$$\begin{gathered} f\left(\theta \right)=\sin \theta \\ f\left(30°\right)=\sin 30° \\ f\left(30°\right) =\frac{1}{2} \end{gathered}$$