Question

How do you solve `cos2x=(-5/12)`?

Answer 1

Let `cos alpha =-5/12=>alpha =cos^-1(-5/12)`

Given equation `cos2x=-5/12` becomes

`cos2x=cosalpha`

`=>2x=2npi+-alpha,where " " n in ZZ`

So `x=npi+-alpha/2`

By using calculator we have

`alpha =cos^-1(-5/12)=0.6368pi`
And
`x=npi+-(0.6368pi)/2=np+-0.3184pi`