# How do you determine the exact coordinates of a point on the terminal arm of the angle in standard position given 60 degrees?

May 1, 2017

See explanation.

#### Explanation:

There are infinitely many such points, so to pick one you have to choose a value for the radius $r$. It is the easiest to choose $1$ as the radius.

If you choose the radius, then the point's coordinates can be calculated as:

$\left\{\begin{matrix}x = r \cdot \cos \varphi \\ y = r \cdot \sin \varphi\end{matrix}\right.$

If you substitute the numbers you get:

$\left\{\begin{matrix}x = 1 \cdot \cos 60 \\ y = 1 \cdot \sin 60\end{matrix}\right.$

$\left\{\begin{matrix}x = \frac{1}{2} \\ y = \frac{\sqrt{3}}{2}\end{matrix}\right.$