Q. 14 - Precalculus Enhanced with Graphing Utilities

Question

In problems 11-26, use the fact that the trigonometric function are periodic to find the exact value of each expression. Do not use a calculator.

$\sin 390°$

Step-by-Step Solution

Answer

The exact value is $\frac{1}{2}$.

Step 1. Given information.

We have:

$\sin \left({390}^{\circ \hspace{0.17em}}\right)$

Step 2. Find the exact value of trigonometric function.

The function is $\sin \left({390}^{\circ \hspace{0.17em}}\right)$.

Formula used:

$\sin \left(\theta +2\pi \right)=\sin \theta$

Here, $\theta =30°$

$$\begin{gathered} \sin \left(30°+360°\right)=\sin 30° \\ =\frac{1}{2} \end{gathered}$$