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$\left(g·p\right)\left(60°\right)$.

Short answer

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

Step-by-step solution

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.

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