Question

find the terminal point p(x, y) on the unit circle determined by the given value of t.
(t = \frac{5pi}{3})
(p(x, y)=(quad))

Explanation:

Step1: Recall unit - circle formulas

For a unit circle $x = \cos t$ and $y=\sin t$, where $t$ is the angle measured counter - clockwise from the positive $x$ - axis.

Step2: Find the value of $x$

We know that $x = \cos t$, and $t=\frac{5\pi}{3}$. Since $\cos\frac{5\pi}{3}=\cos(2\pi-\frac{\pi}{3})=\cos\frac{\pi}{3}=\frac{1}{2}$.

Step3: Find the value of $y$

We know that $y = \sin t$, and $t = \frac{5\pi}{3}$. Since $\sin\frac{5\pi}{3}=\sin(2\pi-\frac{\pi}{3})=-\sin\frac{\pi}{3}=-\frac{\sqrt{3}}{2}$.

Answer:

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