Question

determine the point (x, y) on the unit circle associated with the following real number s. write the exact answer as an ordered pair. do not round.

s = -\frac{3pi}{4}

Explanation:

Step1: Recall unit - circle formula

The coordinates of a point $(x,y)$ on the unit circle associated with a real number $s$ are given by $x = \cos(s)$ and $y=\sin(s)$.

Step2: Calculate the x - coordinate

We know that $x=\cos(s)$, and $s =-\frac{3\pi}{4}$. Since $\cos(-\alpha)=\cos(\alpha)$, then $x = \cos(-\frac{3\pi}{4})=\cos(\frac{3\pi}{4})=-\frac{\sqrt{2}}{2}$.

Step3: Calculate the y - coordinate

We know that $y = \sin(s)$, and $s=-\frac{3\pi}{4}$. Since $\sin(-\alpha)=-\sin(\alpha)$, then $y=\sin(-\frac{3\pi}{4})=-\sin(\frac{3\pi}{4})=-\frac{\sqrt{2}}{2}$.

Answer:

$(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2})$