Q 113. - 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 the function $\left(p·g\right) \left(315°\right)$.

Step-by-Step Solution

Answer

The value of the function $\left(p·g\right) \left(315°\right)$ is $-\frac{1}{2}$.

Step 1. Given information.

Given $f\left(x\right)=\sin x ,g\left(x\right)=\cos x$ and $h\left(x\right)=2x ,P\left(x\right)=\frac{x}{2}$and the value of $x$ is $315°$.

Step 2. Simplify the given expression.

$\left(p·g\right) \left(315°\right)$ can be written as $p\left(315°\right)$ and $g\left(315°\right)$.

Substitute $\sin 315°$ for $p\left(315°\right)$ and $\cos 315°$for $g\left(315°\right)$.

$\left(p·g\right) \left(315°\right)=\left(\sin 315°·\cos 315°\right)$

Step 3. Find the value of p · g   315 ° .

In trigonometric standard angle the value of $\sin 315°$ is $-\frac{1}{\sqrt{2}}$ and the value of $\cos 315°$ is $\frac{1}{\sqrt{2}}$.

Substitute the value of angles in the simplified expression.

$$\begin{gathered} \left(p·g\right) \left(315°\right)=\left(\sin 315°·\cos 315°\right) \\ =\left(-\frac{1}{\sqrt{2}}·\frac{1}{\sqrt{2}}\right) \\ =-\frac{1}{2} \end{gathered}$$