Question

How do you find all solutions to `cos( x+pi/6)=-0.5` on [0,2pi)?

Answer 1

`(13pi)/12 and (5pi)/12`.

Explanation:

Cosine is negative for angles in the 2nd and the 3rd quadrants
`cos(pi+-a)=-cos a`..

From the given equation,
`x+pi/6=arc cos (-1/2), pi+-arc cos(1/2)= pi+-pi/3`.

`x= pi+-pi/3-pi/4`
`=pi(1+1/3-1/4) and pi(1-1/3-1/4)`
`=(13pi)/12 and (5pi)/12`.