Question

Determine the point (x, y) on the unit circle associated with the following real numbers. Write the exact answer as an ordered pair. Do not round.5xS-3

Answer 1

Given:

$s=-\frac{5\pi}{3}$

To find the point (x,y) on the unit circle:

The coordinate of the unit circle can be derived by,

$(\cos s,\sin s)$

Substituting the value of s, we get

$\begin{gathered} (\cos (-\frac{5\pi}{3}),\sin (-\frac{5\pi}{3}))=(\cos (2\pi-\frac{5\pi}{3}),\sin (2\pi-\frac{5\pi}{3})) \\ =(\cos (\frac{\pi}{3}),\sin (\frac{\pi}{3})) \\ =(\frac{1}{2},\frac{\sqrt[]{3}}{2}) \end{gathered}$

Hence, the coordinate point on the unit circle is,

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