Q 103. - 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 $2f\left(\theta \right)$.

Step-by-Step Solution

Answer

The value of the function $2f\left(\theta \right)$ is $\sqrt{3}$.

Step 1. Given information.

Consider the given information $2f\left(\theta \right)$ where $f\left(\theta \right)=\sin \theta$and the value of $\theta =60°$.

Step 2. Finding 2 f θ .

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

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

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