SOLUTION: use the following information to determine sin (2x) tan(x) = 3 and sin (x) is positive sin(2x) =?

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Question 812209: use the following information to determine sin (2x)
tan(x) = 3 and sin (x) is positive
sin(2x) =?
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
use the following information to determine sin (2x)
tan(x) = 3 and sin (x) is positive
***
reference angle is in quadrant I
hypotenuse of reference right triangle=√(1^2+3^2)=√10
sinx=1/√10=√10/10
cosx=3/√10=3√10/10
sin 2x=2sinxcosx=2*√10/10*3√10/10=6*10/100=0.6
..
Check: (w/calculator)
tanx=3
x≈71.565˚
2x≈143.1301
sin2x≈sin(143.1301˚)≈0.6000..
Exact value as determined=0.6000