Question 967184
Find sin 2x, cos 2x, and tan 2x from the given information.
tan x = −1/6, cos x > 0 
reference angle x is in quadrant IV where cos>0, sin<0
hypotenuse of reference right triangle in quadrant IV=&#8730;(6^2+1^2)=&#8730;(36+1)=&#8730;37
sinx=-1/&#8730;37=-&#8730;37/37
cosx=6/&#8730;37=(6&#8730;37)/37
..
sin(2x)=2sinxcosx=2*-&#8730;37/37*6&#8730;37/37=-444/1369
cos(2x)=cos^2(x)-sin^2(x)=36/37-1/37=35/37
tan(2x)=sin(2x)/cos(2x)=16428/47915
..
Check:
tanx=1/6(Q4)
x=350.538
2x=701.075
..
sin(2x)=sin(701.075)=-0.3243
exact value as computed=-444/1369&#8776;-0.3243
..
cos(2x)=cos(701.075)=0.9459
exact value as computed=35/37&#8776;0.9459