Chris H.

asked • 11/16/21

If sin(theta)=-12/37 and theta is between pi and 3pi/2, find the exact value of sin(2theta)

What are the steps that I would take to solve this? I've been trying to come up with a conversion for a while and I am so lost!

Vasile P.

tutor
Draw an angle in 3rd quadrant, draw a right triangles which have a leg 12 and hypothenuse 37. By Pythagorean theorem you can find the other leg. Now use this triangle to find cos of your angle and finally use double angle formula to sing sin(2theta)
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11/16/21

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Raymond B. answered • 11/16/21

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sin2x = 2sinxcosx


sinx = -12/37 cosx = -35/37


sin2x = 2(-12/37)(-35/37) = 24(35)/37^2 = 840/1369


to check the answer find x with a calculator with inverse sin function. x= about 180+18.9= 198.9


2x = 2(198.9) = 397.8 degrees

sin397.8 = sin37.8= .61 = about 840/1369

x was in the 3rd quadrant, but 2x was in the 1st quadrant.




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