SOLUTION: Solve the equation in the interval [0,2pi): 2 cos^2 theta + 3 cos theta + 1 = 0.

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Question 451563: Solve the equation in the interval [0,2pi): 2 cos^2 theta + 3 cos theta + 1 = 0.
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
2 cos^2 theta + 3 cos theta + 1 = 0
To solve, let x = costheta
So we have
2x^2 + 3x + 1 = 0
Solve using the quadratic formula:
x = (-3 +- sqrt(9 - 8))/4
This gives x = -1/2, x = -1
So we need to find the values of theta on the interval [0,2pi) which satisfy
costheta = -1/2, -1
cospi = -1, one of the zeros is pi
cos(2pi/3) = cos(4pi/3) = -1/2
So the zeros are: theta = (2/3)pi,pi,(4/3)pi
The graph is below:
graph%28400%2C400%2C-5%2C5%2C-2%2C6%2C2%2A%28cos%28x%29%29%5E2%2B3%2Acos%28x%29%2B1%29