Question

Find the terminal point on the unit circle determined by5pi/ 6 radians.Use exact values, not decimal approximations.

Answer 1

Recall that the coordinates of the terminal points are

$x=\cos \theta\text{ and y=sin}\theta$$\text{Given that }\theta=\frac{5\pi}{6}\text{ radian.}$$\text{Substitue }\theta=\frac{5\pi}{6}\text{ in x=cos}\theta\text{ to compute x.}$$x=\cos (\frac{5\pi}{6})$

$=\cos (\pi-\frac{\pi}{6})$$\text{Use cos(}\pi-\theta)=-\cos \theta\text{.}$

$=-\cos (\frac{\pi}{6})$

$Use\text{ }\cos (\frac{\pi}{6})=\frac{\sqrt[]{3}}{2}$$x=-\frac{\sqrt[]{3}}{2}$

$\text{Substitue }\theta=\frac{5\pi}{6}\text{ in y=sin}\theta\text{ to compute y.}$$y=\sin (\frac{5\pi}{6})$$=\sin (\pi-\frac{\pi}{6})$

$\text{Use sin(}\pi-\theta)=\sin \theta.$

$=\sin (\frac{\pi}{6})$$Use\text{ }\sin (\frac{\pi}{6})=\frac{1}{2}\text{.}$$y=\frac{1}{2}$

Hence the terminal point is

$(x,y)=(-\frac{\sqrt[]{3}}{2},\frac{1}{2})$

Option third is correct.