Question

The point on the unit circle that corresponds to$\theta =\frac{\pi }{2}$is$P=$_________.

Short answer

The point on the unit circle that corresponds to$\theta =\frac{\pi }{2}$is$P=\left(0,1\right)$.

Step-by-step solution

Given information

The main objective is to find the point on the unit circle at$\theta =\frac{\pi }{2}$.

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 $\theta =\frac{\pi }{2}$.

$$\begin{gathered} \cos \left(\frac{\pi }{2}\right)=0 \\ \sin \left(\frac{\pi }{2}\right)=1 \end{gathered}$$

Therefore, the point is$\left(0,1\right).$