trig
posted by Amanda on .
solve the equation of the domain 0¡Ü¦È¡Ü2¦Ð
3cos^2theta  5costheta 1 = 3sin^2theta

3 cos ^ 2 theta  5 cos theta  1  3 sin ^ 2 theta = 0
3 cos ^ 2 theta  5 cos theta  1  3 ( 1  cos ^ 2 theta ) = 0
3 cos ^ 2 theta  5 cos theta  1  3 + 3 cos ^ 2 theta = 0
6 cos ^ 2 theta  5 cos theta  4 = 0
Substitute :
u = cos theta
6 u ^ 2  5 u  4 = 0
The exact solutons are :
u = cos teta = 4 / 3 = 1.333
and
u = cos theta =  1 / 2
cosine can't be great of 1
so the solutions are :
cos theta =  1 / 2
theta = ( 2 / 3 ) pi = 120 °
and
theta = ( 4 / 3 ) pi = 240 °
If you don't know hov to solve equation:
6 u ^ 2  5 u  4 = 0
In google type:
quadratic equation online
When you see list of results click on:
Free Online Quadratic Equation Solver:Solve by Quadratic Formula
When page be open in rectangle type:
6 u ^ 2  5 u  4 = 0
and click option: solve it!
You wil see solution stepbystep