SOLUTION: sin(x)=8/17 find the exact value of tan(2x) pie/2 <x<pie

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Question 850302: sin(x)=8/17 find the exact value of tan(2x)
pie/2
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
sin(x)=8/17 find the exact value of tan(2x)
reference angle in quadrant II in which sin>0, cos<0, tan<0
Identity: tan%282x%29=2tanx%2F%281-tan%5E2%28x%29%29
cos%28x%29=-sqrt%281-sin%5E2%28x%29%29=-sqrt%281-64%2F289%29=-sqrt%28225%2F289%29=-15%2F17
tan(x)=sin/cos=-8/15

calculator check:
sinx=8/17 (in quadrant II)
x≈151.93˚
2x=303.86
tan(2x)=tan(303.86)≈-1.490
exact value=-(16/15)/(161/225)≈-1.490