Question

What are the coordinates for the point `p((5pi)/6)` where `p(theta)=(x,y)` is the point where the terminal arm of an angle `theta` intersects the unit circl?

Answer 1

`p((5pi)/6)=(-sqrt(3)/2,1/2)`

Explanation:

`(5pi)/6` has reference angle `pi/6` because `pi-(5pi)/6 = pi/6`.

So we know that:
`|cos((5pi)/6)| = cos(pi/6) = sqrt(3)/2`
`|sin((5pi)/6)| = sin(pi/6) = 1/2`

Since `(5pi)/6 in` QII, we know that `cos((5pi)/6)<0` and `sin((5pi)/6)>0`.

Combining what we know, we have that `p((5pi)/6)=(-sqrt(3)/2,1/2)`.

I recommend memorizing the entire Unit Circle as it's not that difficult and is extremely useful.