trig
posted by lauren .
the question is:
given sec x = 4, tan x < 0, find sin(2x), cos(2x)and tan (2x)

we can see that secx > 0 and tanx < 0,
so x must be in quadrants IV
draw a rightangled triangle in that quadrant where
x = 1, y = 4, and r = √17
sinx = 4/√17
cosx = 1/√17
tanx = 4/1 = 4
you should know that:
sin(2x) = 2sinxcos = 2((4/√17)(1/√17) = 8/17
cos(2x) = cos^2x  sin^2x = 1/17  16/17 = 15/17
tan(2x) = sin(2x)/cos(2x) = (8/17)/(15/17) = 8/15