Question

Find the terminal points P(x,y) on the unit circle determined by the given value t

Answer 1

Given $t, -2\pi\leq t\leq2\pi.$ Then

$$x=\cos t, y=\sin t$$

 The terminal point $P(\cos t, \sin t).$

$$t=\dfrac{3\pi}{4}, x=\cos(\dfrac{3\pi}{4})=-\dfrac{\sqrt{2}}{2}, y=\sin(\dfrac{3\pi}{4})=\dfrac{\sqrt{2}}{2}$$

$$P(-\dfrac{\sqrt{2}}{2}, \dfrac{\sqrt{2}}{2})$$

$$t=-\dfrac{\pi}{3}, x=\cos(-\dfrac{\pi}{3})=\dfrac{1}{2}, y=\sin(-\dfrac{\pi}{3})=-\dfrac{\sqrt{3}}{2}$$

$$P(\dfrac{1}{2}, -\dfrac{\sqrt{3}}{2})$$