How do you solve trigonometric equations by factoring?

1 Answer
Nov 5, 2014

Example

Find theta in [0,2pi) such that 2sin^2theta+sin theta-1=0.

Since

2x^2+x-1=(2x-1)(x+1),

by replacing x by sin theta,

2sin^2theta+sin theta-1=(2sin theta-1)(sin theta+1)=0

=>{(sin theta=1/2 => theta=pi/6"," {5pi}/6),(sin theta=-1 => theta={3pi}/2):}

Hence, the solutions are theta=pi/6, {5pi}/6, {3pi}/2.


I hope that this was helpful.