Question

How do you find the solution to `sintheta+sqrt2=sqrt2/2` if `0<=theta<2pi`?

Answer 1

The answer is `S={5/4pi,7/4pi}`

Explanation:

Let's place `sintheta` on one side of the equation

`sintheta+sqrt2=sqrt2/2`

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

`sintheta` is `<0` in the third and fourth quadrant

Therefore,

`theta=5/4pi , 7/4pi`