Question

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

Answer 1

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:

`{(x=r*cosvarphi),(y=r*sinvarphi):}`

If you substitute the numbers you get:

`{(x=1*cos60),(y=1*sin60):}`

`{(x=1/2),(y=sqrt(3)/2):}`