Question 277867: Could you please show me the steps to solve sin 2 y = cos 4 y for y, where 0 degrees = y or < y < 360 degrees. I'm constantly messing up big time somewhere hopefully steps will help.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! sin 2y = cos4 y for y, where 0 degrees = y or < y < 360 degrees
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sin(2y) = cos^2(2y) - sin^2(2y)
sin(2y) = 1-sin^2(2y) - sin^2(2y) = 1 - 2sin^2(2y)
2sin^2(2y) + sin(2y) - 1 = 0 a quadratic in sin(2y)
(2sin + 1)*(sin - 1) = 0
sin(2y) = -1/2
sin(2y) = 1
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sin(2y) = 1
2y = 90, 450
y = 45, 225
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sin(2y) = -1/2
2y = 210, 330, 570, 690
y = 105, 165, 285, 345
All y values in degrees
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