Question

What are the coordinates ofthe terminal point determined by t= 11(pi)/3

Answer 1

The equation given is

`t=(11\pi)/(3)`

By the definitions of trigonometry functions, the point t has as coordinates

`t(x,y)`

Where

`\begin{gathered} x=\cos \theta \\ y=\sin \theta \\ \text{and } \\ \theta=(11\pi)/(3) \end{gathered}`

The next step is to convert the angle to degree

`(11\pi)/(3)=(11*180)/(3)=660^0`

Then we have

`\begin{gathered} x=\cos 660^0\text{=}(1)/(2) \\ y=\sin 660^0=-\frac{\sqrt[]{3}}{2} \end{gathered}`

Hence the terminal point becomes

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

Therefore the right option is C