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
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quadratic equation online
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Free Online Quadratic Equation Solver:Solve by Quadratic Formula
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6 u ^ 2 - 5 u - 4 = 0
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