SOLUTION: If sinx = -3/5 and x is in quadrant III, then what is sin2x, cos2x, and tan2x?

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
RELATED QUESTIONS
find sin2x, cos2x, and tan2x if sinx= {{{-2/sqrt(5)}}} and x terminates in quadrant... (answered by lwsshak3)

Find sin2x, cos2x, tan2x if sinx= -8/17 and x terminates in quadrant III... (answered by ikleyn)

Find sin2x,cos2x,tan2x if sinx=3/sqrt10 and x terminates in quadrant... (answered by lwsshak3)

Given that cotx=3/5 and x is in quadrant 2, find sin2x,... (answered by ikleyn)

Find cos2x,sin2x , and tan2x if sinx=-12/13 and x terminates in quadrant IV... (answered by lwsshak3)

Find sin2x, cos2x, and tan2x if cosx= -15/17 and x terminates in quadrant... (answered by ikleyn)

Determine the values of sin2x, cos2x, and tan2x: Sinx=3/5, and x is acute (answered by Edwin McCravy)

Given that cotx=-5/6 and x is in quadrant 2, find sin2x,... (answered by ikleyn)

what is the exact value of sin2x, cos2x and tan2x if... (answered by lwsshak3)