Question 1162249
<pre>
Theo apparently does not know the meaning of "exact value".  It means
NO DECIMALS!

[I corrected my typo for tan(&theta;), which was neither asked for nor needed.  My tan(2&theta;) was and is correct.]

{{{
matrix(1,5,sin(theta) =-7/12,"", ",","",180^o < theta < 270^o) }}} 

We draw θ in QIII, with y (opposite side) =-7 and r (hypotenuse) = 12.
We calculate x (adjacent side):

{{{matrix(5,1,
x^2+y^2=r^2,
x^2+(-7)^2=12^2,
x^2+49=144,
x^2=95,
x="" +- sqrt(95))}}}

Since x goes left of the origin, we take the negative answer, 
{{{x=-sqrt(95)}}}

{{{drawing(400,400,-1.5,1.5,-1.5,1.5,
locate(-.75,.14,x=-sqrt(95)), locate(-1.35,-.3,y=-7),
red(locate(-.2,.3,theta)),
line(-2,0,2,0), line(0,-2,0,2), line(-1,-.7181848464,0,0),
locate(-.47,-.34,"r=12"), red(arc(0,0,.5,-.5,0,215)),
line(-1,0,-1,-.7181848464) )}}}

Then to calculate the trig ratios for 2θ, we will need

{{{matrix(3,1,
sin(theta)=opposite/hypotenuse=y/r=-7/12,
cos(theta)=adjacent/hypotenuse=x/r=-sqrt(95)/12,
tan(theta)=adjacent/hypotenuse=y/x=(-7)/(-sqrt(95))=7/sqrt(95)=(7sqrt(95))/(sqrt(95)sqrt(95))=7sqrt(95)/95)}}}


{{{matrix(3,1,
sin(2theta)=2sin(theta)cos(theta)=2(-7/12)(-sqrt(95)/12)=7sqrt(95)/72,
cos(2theta)=cos^2(theta)-sin^2(theta)=(-sqrt(95)/12)^2-(-7/12)^2=95/144-49/144=46/144=23/72,
tan(2theta)=sin(2theta)/cos(2theta)=(7sqrt(95)/72)/(23/72)=7sqrt(95)/23)}}}

Edwin</pre>