SOLUTION: cos theta = - sqrt55/8 and 90 degrees < theta < 180 degrees. Find sin 2theta

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Question 994584: cos theta = - sqrt55/8 and 90 degrees < theta < 180 degrees. Find sin 2theta
Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
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cos theta = - sqrt55/8 and 90 degrees < theta < 180 degrees. Find sin 2theta.
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Probably,  the condition is read as  cos%28theta%29 = -sqrt%2855%29%2F8.

OK,  if so,  then

sin%28theta%29 = sqrt%281+-+cos%5E2%28theta%29%29 = sqrt%281+-+55%2F64%29 = sqrt%289%2F64%29 = 3%2F8.

The sign is  "plus"  since the angle  theta  is in the second quadrant.

Then  sin%282%2Atheta%29 = 2%2Asin%28theta%29%2Acos%28theta%29 = -2%2A%283%2F8%29%2A%28sqrt%2855%29%2F8%29 = -%283%2Asqrt%2855%29%29%2F32.