Question

Without solving, how do you determine the number of solutions for the equation `sintheta=sqrt3/2` in `0<=theta<2pi`?

Answer 1

2 solutions
`theta=pi/3` and `theta=2pi/3`

Explanation:

`pi/3` is a remarkable angle for the sinus function and `sin(pi/3)=root2(3)/2`

on the other hand we know that `sin(pi-theta)=sin(pi)cos(theta)-cos(pi)sin(theta)=sin(theta)`. This implies that if there is a solution at `theta=pi/3`, there must be another solution at `theta=2pi/3`