Question

How do you find the exact value of `cos^-1 (-1)`?

Answer 1

for angles in the range `[0,2pi]`
`cos^-1(-1) = pi` (radians)

Explanation:

If `cos^(-1)= theta`
`rArrcolor(white)("XXXXX")cos(theta) = -1`

This means that the adjacent side is equal in magnitude to the hypotenuse but negative.

Within the range `[0,2pi]`
this is only true at `theta=pi (= 180^@)`

For all solutions (unrestricted in range:
`color(white)("XXX")cos^-1(-1)=pi+n2picolor(white)("XXX")AAn in ZZ`