Question

Find sin 2x, cos 2x, and tan 2x from the given infomation

csc x=4, tan x < 0

Answer 1

csc positive, tan negative means QII

since sinx = 1/cscx,

sinx = 1/4
cosx = √15/4
tanx = 1/√15

Now just apply your double-angle formulas

Answer 2

thanks but I'm still stumped by what they mean about how and what the double angle formula is. The double angle formula confuses me

Answer 3

sin2x = 2 sinx cosx
= 2(1/4)(√15/4) = 2√15/16

cos2x = cos^2x - sin^2 x
= 15/16 - 1/16 = 7/8

tan2x = 2tanx/(1-tan^2 x)
= 2/√15 / (1 - 1/15)
= 2/√15 * 15/14
= √15/7