Question

Find sin 2x, cos 2x, and tan 2x from the given information. cot x = 3/5, x in Quadrant I

Answer 1

x in first quadrant
cot x = -3/5 --> tan x = -5/3
1) Use the trig identity: tan 2a = (2tan x)/(1 - tan^2 x)
tan 2x = (-10/3):(1 - 25/9) = 15/8
2) Find cos 2x. Use the trig identity: tan^2 x = (1 - cos 2x)/(1 + cos 2x)
25/9 = (1 - cos 2x)/(1+ cos 2x)
25 + 25*cos 2x = 9 - 9*cos 2x
34*cos 2x = -16 -> cos 2x = -16/34
3) sin 2x = tan 2x*cos 2x = (15/8):(-16/34) = -15/17