Posted by Abby on Wednesday, March 23, 2011 at 10:22pm.
tan(x)=5 sin(x) for interval π < x < π
A) 0, 1.571 B) 1.571, 0, 1.571 C) 1.369, 0, 1.369 D) 0, 1.369

Pre Calc  Jai, Wednesday, March 23, 2011 at 10:37pm
recall that tan(x) can be rewritten as
tan (x) = sin (x) / cos (x)
substituting:
sin(x) / cos(x) = 5 sin(x)
the sin(x) will be cancelled:
1/cos(x) = 5
cos(x) = 1/5
solving this,
x = +/ 1.369
since it must be on interval π < x < π
x =  1.369 
Pre Calc  Reiny, Wednesday, March 23, 2011 at 10:39pm
are we solving ????
tanx = 5sinx
sinx/cosx= 5sinx
sinx = 5sinxcosx
sinx  5sinxcos)=0
sinx(1  5cosx) = 0
sinx = 0 or cosx = 1/5
if sinx = 0, x = 0, π or 2π
if cosx = 1/5, x = 1.369 or 1.369 if π < x < π
so for the given domain
x = 1.369 , 0, 1.369 , which would be choice C) 
Pre Calc  Abby, Wednesday, March 23, 2011 at 10:52pm
Thanks so much guys!!!!

Pre Calc  Reiny, Wednesday, March 23, 2011 at 10:58pm
Did you notice that Jai missed one of the answers of
x = 0.
You should not cancel sinx , but rather use it as one of the factors.
by canceling sinx , he "lost" the answer to sinx = 0 
Pre Calc  Jai, Wednesday, March 23, 2011 at 11:18pm
oh yeah,, sorry about that. 0 is also a solution~
thanks for correcting me, sir~ :)