Posted by **lauren** on Wednesday, January 19, 2011 at 6:40pm.

the question is:

given sec x = 4, tan x < 0, find sin(2x), cos(2x)and tan (2x)

- trig -
**Reiny**, Wednesday, January 19, 2011 at 7:11pm
we can see that secx > 0 and tanx < 0,

so x must be in quadrants IV

draw a right-angled 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

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