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 = 225°

Explanation:

Step1: Recall unit - circle coordinates formula

For a point $(x,y)$ on the unit circle associated with an angle $\theta$ (in degrees), $x = \cos\theta$ and $y=\sin\theta$. Here $\theta = 225^{\circ}$.

Step2: Convert degrees to radians

To use the trigonometric functions on a calculator or from known values, convert $225^{\circ}$ to radians. We know that $1^{\circ}=\frac{\pi}{180}$ radians, so $225^{\circ}=225\times\frac{\pi}{180}=\frac{5\pi}{4}$ radians.

Step3: Find the x - coordinate

$x = \cos(225^{\circ})=\cos(\frac{5\pi}{4})=-\frac{\sqrt{2}}{2}$.

Step4: Find the y - coordinate

$y=\sin(225^{\circ})=\sin(\frac{5\pi}{4})=-\frac{\sqrt{2}}{2}$.

Answer:

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