Question

How do you find the solution to `2sin^2theta+sintheta-1=0` if `0<=theta<360`?

Answer 1

The solutions are `S={30º,150º,270º}`

Explanation:

The equation is `2sin^2theta+sintheta-1=0`

We can factorise the LHS

`(2sintheta-1)(sintheta+1)=0`

Therefore,

`sintheta=-1`, `=>`, `theta=270º`

`sintheta=1/2`, `=>`, `theta=30º, 150º`