Friday

April 18, 2014

April 18, 2014

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 °

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 step-by-step

**Related Questions**

Trig - Find all values of theta in the interval 0 <= theta < 360 that ...

trig - establish identity 5csc^2theta-3cot^2theta=2csc^2theta+3

Calculus - 2sin(2theta) + sqrt(3) = 0 interval (0,2pi) How do I solve this? I ...

math (final trig problem) - Solve for x on the interval [0,π/2): cos^3(2x...

trig - tan^2theta+6=sec^2theta+5

trigonometry - convert the polar equation r^2=2cos^2theta + 3sin^2theta into a ...

Math - Trig Substitution - How can I solve the integral of x^3√(9-x^2) dx ...

Trig - Cos(2theta)=-1/2 There are 6 solutions, how do i solve this?

Precalculus with Trigonometry - What values of theta between 0 and 2pi solve the...

Trigonometry - find all values of theta in the interval 0<theta<360 that ...