Q 105. - 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 $f\left(-\theta \right)$.

Step-by-Step Solution

Answer

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

Step 1. Given information.

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

Step 2. Finding f - θ .

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

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

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