Question

Solve the equation `cos(pi/6-x)=-1/2` in the interval `[0,2pi)`?

Answer 1

`(5pi)/6` and `(3pi)/2`

Explanation:

As `cos((2pi)/3)=-1/2`, we can write the equation as

`cos(pi/6-x)=cos((2pi)/3)`

and hence genera solution is `pi/6-x=2npi+-(2pi)/3`, where `n` is an integer

i.e. `x=2kpi+pi/6+-(2pi)/3`, where `k` is an integer (note `k=-n`).

and between `[0,2pi)`, the solution is `pi/6+(2pi)/3=(5pi)/6`

and `2pi+p/6-(2pi)/3=(3pi)/2`