SOLUTION: Please help me out with this problem! Solve for all solutions of t on the interval [0,2pi) 2-2sin(t)=2sqrt( 3 )cos(t)

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Question 993622: Please help me out with this problem! Solve for all solutions of t on the interval [0,2pi)
2-2sin(t)=2sqrt( 3 )cos(t)
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me out with this problem! Solve for all solutions of t on the interval [0,2pi)
2-2sin(t)=2sqrt(3)cos(t)
1+-+sin%28t%29+=+sqrt%283%29%2Acos%28t%29
Square both sides.
1+-+2sin%28t%29+%2B+sin%5E2%28t%29+=+3cos%5E2%28t%29
Sub 1 - sin^2 for cos^2
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1+-+2sin%28t%29+%2B+sin%5E2%28t%29+=+3+-+3sin%5E2%28t%29
4sin%5E2%28t%29+-+2sin%28t%29+-+2+=+0
2sin%5E2%28t%29+-+sin%28t%29+-+1+=+0
(2sin + 1)*(sin - 1) = 0
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sin(t) = 1
t = pi/2
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sin(t) = -1/2
t = 7pi/6, 11pi/6