Q.10 - Precalculus Enhanced with Graphing Utilities

Question

The point on the unit circle that corresponds to $\theta =\frac{\pi }{3}$ is $P=$________.

Step-by-Step Solution

Answer

The point on the unit circle that corresponds to $\theta =\frac{\pi }{3}$ is $P=\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)$.

Given information

The main objective is to find the point on the unit circle at $\theta =\frac{\pi }{3}$.

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 $\theta =\frac{\pi }{3}$.

$$\begin{gathered} \cos \left(\frac{\pi }{3}\right)=\frac{1}{2} \\ \sin \left(\frac{\pi }{3}\right)=\frac{\sqrt{3}}{2} \end{gathered}$$

The point is $\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)$.