Question 715621: If sinx = -3/5 and x is in quadrant III, then what is sin2x, cos2x, and tan2x?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! If sinx = -3/5 and x is in quadrant III, then what is sin2x, cos2x, and tan2x?
let O=opposite side
let A=adjacent side
H=hypotenuse
..
sin x=-3/5=O/H
O=-3, H=5
A=√(H^2-O^2)
=√(5^2-3^2)
=√(25-9)
=√16
A=-4 (In quadrant III where cos<0)
cos x=A/H=-4/5
tanx=O/A=-3/-4=3/4
..
Identity:sin2x=2sinxcosx
=2*-3/5*-4/5
sin2x=24/25
..
Identity:cos2x=cos2^x-sin^2x
=(-4/5)^2-(-3/5)^2
=16/25-9/25
cos 2x=7/25
..
Identity: tan2x=(2tanx)/(1-tan^2x)
=(2*3/4)/(1-(3/4)^2)
=(6/4)/(1-9/16)
=(3/2)/(7/16)
tan2x=24/7
|
|
|
