Question

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

Short answer

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

Step-by-step solution

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