SOLUTION: Find sin2x, cos2x, and tan2x if cosx= -15/17 and x terminates in quadrant III

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Question 995648: Find sin2x, cos2x, and tan2x if cosx= -15/17 and x terminates in quadrant III
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
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Find sin2x, cos2x, and tan2x if cosx= -15/17 and x terminates in quadrant III.
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sin(x) = sqrt%281+-+cos%5E2%28x%29%29 = sqrt%281+-+%28-15%2F17%29%5E2%29 = sqrt%281+-+%28225%2F289%29%29 = sqrt%28%28289-225%29%2F289%29%29 = sqrt%2864%2F289%29 = (-8/17).

The sign is  "minus"  because the angle is in the quadrant III.

Now,  sin(2x) = 2*sin(x)*cos(x) = 2.%28-8%2F17%29.%28-15%2F17%29 = (*)     (calculate yourself).

cos(2x) = sqrt%281-sin%5E2%282x%29%29 = (**)     (calculate yourself using (*)).

tan(2x) = %28sin%282x%29%29%2F%28cos%282x%29%29 = calculate yourself using (*) and (**).