posted by Anonymous .
Given that tan x= -3/4 and x is in the second quadrant. Find sin 2x, cos 2x, and tan 2x (Exact, no decimals).
Please show step-by-step, thank you!
construct a triangle in quad II with x=-4 and y = 3
since tanØ = y/x or opposite/adjacent
so r^2 = (-4)^2 + 3^2
r = 5
sinx = 3/5 and cosx = -4/5
you have to know that
sin 2x = 2sinxcosx = 2(3/5)(-4/5) = -24/25
cos 2x = cos^2 x - sin^2 x = 16/25 - 9/25 = 7/25
tan 2x = sin 2x/ cos 2x = (-24/25) / (7/25) = -24/7