trig
posted by Amanda .
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
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 stepbystep
Respond to this Question
Similar Questions

Math  Trig Substitution
How can I solve the integral of x^3√(9x^2) dx using trigonometric substitution? 
maths
if cot theta =7/8 , evaluate (1+sin^2theta)(1sin^2theta)/(1+cost^2theta)(1+co^2theta) the answer should be 49/64 but i couldn't get that answer. can any one help? 
trigonometry
convert the polar equation r^2=2cos^2theta + 3sin^2theta into a rectangular equation 
Calculus
2sin(2theta) + sqrt(3) = 0 interval (0,2pi) How do I solve this? 
trig
establish identity 5csc^2theta3cot^2theta=2csc^2theta+3 
Math
Prove: [(tan^2theta+1)(cos^2theta1)]=1sec^2theta 
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) 
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 … 
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 
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: …