If tan α = 9 and α is acute, find the exact value of sin 2α.

we use a for alpha... 

tan(a)=sin(a)/cos(a)=9 
and 
tan(a)=9=9/1 
and thus y=9 , x=1, r=sqrt(82) 
so that 
sin 2a = 
2sin(a)*cos(a)=
2(y/r)(x/r)=
2(9)(1)/82=9/41