How do you find the solution to 6cos^2theta+5costheta-4=0 if 0<=theta<360?

1 Answer
May 25, 2018

The solutions are S={60^@, 300^@} for theta in [0, 360)

Explanation:

This is a quadratic equation in costheta

6cos^2theta+5costheta-4=0

The discriminant is

Delta=b^2-4ac=5^2-4(6)(-4)=121

As Delta >0, there are 2 real solutions

{(costheta_1=(-5+sqrt121)/(12)=(-5+11)/12),(costheta_2=(-5-sqrt121)/(12)=(-5-11)/12):}

{(costheta_1=6/12=1/2),(costheta_2=-1.33):}

{(theta_1=60^@ ;300^@),(theta_2=O/):}

The solutions are S={60^@, 300^@} for theta in [0, 360)