Question

How do you find the coordinates of the terminal points corresponding to the following arc length on the unit circle: $-\frac{\mathrm{\pi }}{6}$?

Answer 1

Coordinates of terminal points:

We know that in a unit circle the coordinates of terminal points of any length $\theta$ are $\left(x,y\right):\left(\cos \left(\theta \right),\sin \left(\theta \right)\right)$

The given arc length is $-\frac{\mathrm{\pi }}{6}$.

So the coordinates are :-

$\begin{array}{rcl}x& =& \cos \left(-\frac{\mathrm{\pi }}{6}\right)=\frac{\sqrt{3}}{2}\end{array}$ and $y=\sin \left(-\frac{\mathrm{\pi }}{6}\right)=-\frac{1}{2}$

Therefore the coordinates are :-

$\left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right)$..