SOLUTION: what is the exact value of sin2x, cos2x and tan2x if sinx=3/5,0<x<pi/2

Question 916475: what is the exact value of sin2x, cos2x and tan2x if sinx=3/5,0
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
what is the exact value of sin2x, cos2x and tan2x if sinx=3/5, 0 < x < π/2
***
You are working with a 3-4-5 reference right triangle in quadrant I.
sinx=3/5
cosx=4/5
..
sin2x=2sinxcosx=2*3/5*4/5=24/25
cos2x=cos^2x-sin^2x=16/25-9/25=7/25
tan2x=sin2x/cos2x=24/7
check:
sinx=3/5
x=36.87
2x=73.74˚
..
sin2x=sin(73.74˚)≈0.9600...w/calculator:
exact value=24/25≈0.9600...as computed
..
coss2x=cos(73.74˚)≈0.2800...w/calculator:
exact value=7/25≈0.2800...as computed
..
tan2x=tan(73.74˚)≈3.4286...w/calculator:
exact value=24/7≈3.4285...as computed

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