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=(5\pi)/(6)\text{ radian.}`
`\text{Substitue }\theta=(5\pi)/(6)\text{ in x=cos}\theta\text{ to compute x.}`
`x=\cos ((5\pi)/(6))`

`=\cos (\pi-(\pi)/(6))`
`\text{Use cos(}\pi-\theta)=-\cos \theta\text{.}`

`=-\cos ((\pi)/(6))`

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

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

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

`=\sin ((\pi)/(6))`
`Use\text{ }\sin ((\pi)/(6))=(1)/(2)\text{.}`
`y=(1)/(2)`

Hence the terminal point is

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

Option third is correct.