Q. 9 - Precalculus Enhanced with Graphing Utilities

Question

The point on the unit circle that corresponds to $\theta =\frac{\pi }{4}$ is $P=$_____________.

Step-by-Step Solution

Answer

The point on the unit circle that corresponds to $\theta =\frac{\pi }{4}$ is $P=\left(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)$.

Given information

The main objective is to find the point on the unit circle at $\theta =\frac{\pi }{4}.$.

Evaluate

The point on a unit circle that corresponds to $\theta$ is defined as $\left(x,y\right)=\left(\cos \theta ,\sin \theta \right)$.

Find $\cos \theta ,\sin \theta$ at $\theta =\frac{\pi }{4}$.

$\begin{array}{rcl}\cos \left(\frac{\pi }{4}\right)& =& \frac{\sqrt{2}}{2}\\ \sin \left(\frac{\pi }{4}\right)& =& \frac{\sqrt{2}}{2}\end{array}$

The point is $\left(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)$.