Question

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

Answer 1

The solutions are `S={45º, 135º, 225º,315º}`

Explanation:

Let's rewrite the equation

`2sin^2theta-1=0`

`2sin^2theta=1`

`sintheta=+-1/sqrt2=+-sqrt2/2`

When `sintheta=sqrt2/2`, `=>`, `theta=45º, 135º`

and when `sintheta=-sqrt2/2`, `=>`, `theta=225º, 315º`