Question

solve the equation of the domain 0¡Ü¦È¡Ü2¦Ð
3cos^2theta - 5costheta -1 = 3sin^2theta

Answer 1

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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