How do you solve the equation 2cos^2theta-3costheta+1=0 for 0<=theta<2pi?

1 Answer
Nov 21, 2016

The solutions are S={0,pi/3,(5pi)/3}

Explanation:

Let's factorise the LHS

2cos^2theta-3costheta+1=(2costheta-1)(costheta-1)=0

Therefore, 2costheta-1=0

costheta=1/2

and costheta-1=0

cos theta=1

We are looking for theta in [0, 2pi[

When costheta=1/2

theta=pi/3 , (5pi)/3

When costheta=1

theta=0