Question 467010
Find the exact value of sin(2theta) if csc (theta) = -4 and 180<theta<270
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csc = r/y = -4/1
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So, r = 4 and y = -1  
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Then x = sqrt[4^2 - 1^2] = sqrt(15)
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Note: x may be positive or negative depending
on whether theta is in the 3rd or 4th Quadrant
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sin(2theta) = 2sin(theta)*cos(theta)
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If x is negative, cos(theta) = x/r = -sqrt(15)/4
and sin(2theta) = 2(-1/4)(-sqrt(15)/4) = sqrt(15)/8
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If x is positive, cos(theta) = x/r = sqrt(15)/4
and sin(2theta) = 2(-1/4)(sqrt(15)/4) = -sqrt(15)/8
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Cheers,
Stan H.
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