Q. 11 - 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.

$\sin 405°$

Step-by-Step Solution

Answer

The exact value is $\frac{\sqrt{2}}{2}$.

Step 1. Given information.

We have:

$\sin 405°$

Step 2. Find the exact value of trigonometric function.

The function is $\sin 405°$.

Formula used:

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

Here, $\theta =45°$

$$\begin{gathered} \sin \left(45°+360°\right)=\sin 45° \\ =\frac{\sqrt{2}}{2} \end{gathered}$$