Question

Question #d85ec

Answer 1

`360n+-111.5` for any integer n

Explanation:

Substitute `a=cosx`
`2a^2-2a-1=0`

Using the quadratic formula
`a=(2+-sqrt(4+8))/4`
`a=(1+-sqrt(3))/2`

Substitute `a=cosx` once again
`cosx=(1+-sqrt(3))/2`
We know `cosx` cannot exceed 1, so `(1+sqrt3)/2` is not an answer.
`cosx=(1-sqrt(3))/2`

Solve for x, (using a calculator)
`x=111.5`

Remembering some trig symmetries, `cos(x)=cos(-x)` and that `2pi` can be added and not change the angle, the answer is achieved:
All possible values are `360n+-x` where n is any integer.

So, if you want to stay inside 360 degrees, the answers are 111.5 and 248.5