SOLUTION: if sinx= 3/5 on the interval(pi/2,pi), find the exact value of tan(2x)

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Question 851983: if sinx= 3/5 on the interval(pi/2,pi), find the exact value of tan(2x)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
if sinx= 3/5 on the interval(pi/2,pi), find the exact value of tan(2x)
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Identity: tan%282x%29=2tan%28x%29%2F%281-tan%5E2%28x%29%29
sin(x)=3/5
cos%28x%29=-sqrt%281-sin%5E2%28x%29%29=-sqrt%281-%289%2F25%29%29=-sqrt%2816%2F25%29=-4%2F5
tan(x)=-sin(x)/cos(x)=-3/4

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calculator check:
sin(x)=3/5 (Q2 in which sin>0, cos<0)
x=143.13˚
2x=286.26
tan(2x)=tan(286.26)≈-3.4286…
Exact value=-24/7≈-3.4285...