Q 107. - 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 $\left(f+g\right)\left(30°\right)$.

Step-by-Step Solution

Answer

The value of the function is $\left(\frac{1+\sqrt{3}}{2}\right)$.

Step 1. Given information.

Given$f\left(x\right)=\sin x$ and $g\left(x\right)=\cos x$ and the value of $x$ is $30°$.

Step 2. Simplify the given expression.

$\left(f+g\right) \left(30°\right)$ can be written as $f\left(30°\right)$ and $g\left(30°\right)$.

Substitute $\sin 30°$for $f\left(30°\right)$ and $\cos 30°$for $g\left(30°\right)$.

then,

$\left(f+g\right) \left(30°\right)=\sin 30°+\cos 30°$

Step 3. Find the value of f + g 30 ∘ .

In trigonometric standard angle the value of $\sin {30}^{\circ }=\frac{1}{2}$ and $\cos {30}^{\circ }=\frac{\sqrt{3}}{2}$.

Substitute the values of angles into simplified expression.

$$\begin{gathered} \left(f+g\right) \left(30°\right)=\left(\sin 30°+\cos 30°\right) \\ =\left(\frac{1}{2}+\frac{\sqrt{3}}{2}\right) \\ =\left(\frac{1+\sqrt{3}}{2}\right) \end{gathered}$$