Q.11 - Precalculus Enhanced with Graphing Utilities

Question

For any angle $\theta$ in standard position, let $P=\left(x,y\right)$ be the point on the terminal side of $\theta$ that is also on the circle$x^2+y^2=r^2$.

 Then, $\sin \theta$ =________ and $\cos \theta$ = ________.

Step-by-Step Solution

Answer

For any angle $\theta$in standard position, let $P=\left(x,y\right)$ be the point on the terminal side of $\theta$ that is also on the circle $x^2+y^2=r^2$.

Then,  $\sin \theta =\frac{y}{r},\cos \theta =\frac{x}{r}$.

Given information

Given the circle $x^2+y^2=r^2$ and $P=\left(x,y\right)$ is a point on the circle.

The main objective is to find $\sin \theta ,\cos \theta$.

Evaluate

From the definitions of sine and cosine functions on a circle$x^2+y^2=r^2$ at a point $\left(x,y\right)$, it is clear that $\sin \theta =\frac{y}{r},\cos \theta =\frac{x}{r}.$