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February 8, 2016
Posted by **Amanda** on Monday, April 9, 2012 at 10:29pm.

3cos^2theta - 5costheta -1 = 3sin^2theta

- trig -
**Bosnian**, Monday, April 9, 2012 at 11:00pm3 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 °

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6 u ^ 2 - 5 u - 4 = 0

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6 u ^ 2 - 5 u - 4 = 0

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