# trig

posted by .

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

• trig -

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

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

## Similar Questions

1. ### Math - Trig Substitution

How can I solve the integral of x^3√(9-x^2) dx using trigonometric substitution?
2. ### maths

if cot theta =7/8 , evaluate (1+sin^2theta)(1-sin^2theta)/(1+cost^2theta)(1+co-^2theta) the answer should be 49/64 but i couldn't get that answer. can any one help?
3. ### trigonometry

convert the polar equation r^2=2cos^2theta + 3sin^2theta into a rectangular equation
4. ### Calculus

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

establish identity 5csc^2theta-3cot^2theta=2csc^2theta+3
6. ### Math

Prove: [(tan^2theta+1)(cos^2theta-1)]=1-sec^2theta
7. ### Math

sin theta = 8/17 and theta is in the second quadrant. Find sin(2theta),cos(2theta),tan(2theta) exactly sin(2theta) cos(2theta) tan(2theta)
8. ### Math

sin theta = 8/17 and theta is in the second quadrant. Find sin(2theta),cos(2theta),tan(2theta) exactly sin(2theta) cos(2theta) tan(2theta) sin(2theta) would it be 2 x (8/17) cos(2theta) would be 2 x (15/17) tan(2theta) would be 2 x …
9. ### Precalc+trig

Solve tan(40/90) for the double angle cos(2theta). I know I use the x^2 + y^2 = r^2 formula and cos(2theta) = cos^2theta - sin^2theta. But I don't understand my answer
10. ### Trig

Solve each equation for exact solutions over the interval [0,360)where appropriate. Round approximate solutions to the nearest tenth degree. Sin^2Theta=Cos^2Theta+1 My Work: Using double angle Identity I subtract 1 to other side therefore: …

More Similar Questions