SOLUTION: Find the exact value of each trigonometric expression. sin(2 tan^-1 (-15/8) )  

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Question 1064371: Find the exact value of each trigonometric expression.
sin(2 tan^-1 (-15/8) )


Found 2 solutions by rothauserc, ikleyn:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
take the inverse tangent of -15/8
:
inverse tangent of -15/8 = -61.9275
:
sin(2 * -61.9275) = -0.8305
:

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the exact value of each trigonometric expression.
sin(2 tan^-1 (-15/8) )
~~~~~~~~~~~~~~~~~~~~~~~~~~ 

They want you calculate  sin%282alpha%29,  where alpha = arctan(-15/8)}}} and alpha is in Q4.


So, you know that tan%28alpha%29 = -15%2F8.

Then  sin%28alpha%29 = tan%28alpha%29%2Fsqrt%281+%2B+tan%5E2%28alpha%29%29 = %28%28-15%2F8%29%29%2Fsqrt%281+%2B+%28-15%2F8%29%5E2%29 = %28%28-15%2F8%29%29%2Fsqrt%281+%2B+%28225%2F64%29%29 = %28%28-15%2F8%29%29%2Fsqrt%28289%2F64%29%29 = %28%28-15%2F8%29%29%2F%28%2817%2F8%29%29 = -15%2F17,


      cos%28alpha%29 = sqrt%281-sin%5E2%28alpha%29%29 = sqrt%281-%28-15%2F17%29%5E2%29 = sqrt%281+-+225%2F289%29 = sqrt%2864%2F289%29 = 8%2F17.


Now the last step is:  sin%282alpha%29 = 2%2Asin%28alpha%29%2Acos%28alpha%29 = 2%2A%28-15%2F17%29%2A%288%2F17%29 = -240%2F289.

Solved.