Question 807317
Cosine is positive in quadrant 4, sine is not.


{{{sec(x)=8}}}


Tells is that


{{{r=8}}}  and {{{x=1}}}


so {{{y=sqrt(r^2-x^2)=sqrt(8^2-1^2)=3sqrt(7)}}}


Now we are ready...

{{{sin(2x)=2sin(x)cos(x)=2(-3sqrt(7)/8)(1/8)=-3sqrt(7)/32}}}

{{{cos(2x)=2cos(x)^2-1=2(1/8)^2-1=-31/32}}}


{{{tan(2x)=sin(2x)/cos(2x)=(-3sqrt(7)/32)(-32/31)=3sqrt(7)/31}}}