Q.8 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

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

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 $\left(0,1\right).$