Question

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

Short answer

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

Step-by-step solution

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