SOLUTION: Use the given information to determine the exact trigonometric value. If csc(theta)= -5/2 and 180 degrees < theta < 270 degrees; find the exact value of sin(2theta)

Question 1033300: Use the given information to determine the exact trigonometric value.
If csc(theta)= -5/2 and 180 degrees < theta < 270 degrees; find the exact value of sin(2theta)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Use the given information to determine the exact trigonometric value.
If csc(theta)= -5/2 and 180 degrees < theta < 270 degrees; find the exact value of sin(2theta)
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Note: sin = 1/csc, so sin(t) = y/r = -2/5
In QIII, y is negative.
So, y = -2 and r = 5
Then x = -sqrt[5^2-2^2] = -sqrt[21]
and cos(x) = -sqrt(21)/5
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Ans: sin(2t) = 2*sin(t)cos(5) = 2(-2/5)(-sqrt(21)/5) = -(4/25)sqrt(21)
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Cheers,
stan H.
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