How do you find the point (x,y) on the unit circle that corresponds to the real number t=(5pi)/4?

May 21, 2018

M$\left(- \frac{\sqrt{2}}{2} , - \frac{\sqrt{2}}{2}\right)$

Explanation:

$t = \frac{\pi}{4} + \pi$. --> t is in Quadrant 3
$x = \cos t = - \cos \left(\frac{\pi}{4}\right) = - \frac{\sqrt{2}}{2}$
$y = \sin t = - \left(\sin \frac{\pi}{4}\right) = - \frac{\sqrt{2}}{2}$
Point M(x, y) has as coordinates:
M$\left(- \frac{\sqrt{2}}{2} , - \frac{\sqrt{2}}{2}\right)$