Q 106. - 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 $g\left(-\theta \right)$.

Step-by-Step Solution

Answer

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

Step 1. Given information.

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

Step 2. Finding g - θ .

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

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

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