Question

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

Answer 1

SOLUTION

The equation given is

$t=\frac{11\pi}{3}$

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

$t(x,y)$

Where

$\begin{gathered} x=\cos \theta \\ y=\sin \theta \\ \text{and } \\ \theta=\frac{11\pi}{3} \end{gathered}$

The next step is to convert the angle to degree

$\frac{11\pi}{3}=\frac{11\times180}{3}=660^0$

Then we have

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

Hence the terminal point becomes

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

Therefore the right option is C