Q 112. - Precalculus Enhanced with Graphing Utilities

Question

If $f\left(x\right)=\sin x ,g\left(x\right)=\cos x$ and $h\left(x\right)=2x ,P\left(x\right)=\frac{x}{2}$.Find the value of $\left(g·p\right) \left(60°\right)$.

Step-by-Step Solution

Answer

The value of function $\left(g·p\right)\left(60°\right)$ is $\frac{\sqrt{3}}{4}$.

Step 1. Given information.

Given $f\left(x\right)=\sin x ,g\left(x\right)=\cos x$ and the value of $x$ is $60°$.

Step 2. Simplify the given expression.

$\left(g·p\right) \left(60°\right)$ can be written as $g\left(60°\right)$ and $p\left(60°\right)$.

Substitute $\cos 60°$ for $g\left(60°\right)$ and $\sin 60°$ for$f\left(60°\right)$.

$\left(g·p\right) \left(60°\right)=\left(\cos 60°·\sin 60°\right)$

Step 3. Find the value of g · p   60 ° .

In trigonometric standard angle the value of $\cos 60°=\frac{1}{2}$ and the value of $\sin 60°=\frac{\sqrt{3}}{2}$.

Substitute the values of angles in simplified expression.

$$\begin{gathered} \left(g·p\right) \left(60°\right)=\left(\cos 60°·\sin 60°\right) \\ =\left(\frac{1}{2}·\frac{\sqrt{3}}{2}\right) \\ =\frac{\sqrt{3}}{4} \end{gathered}$$