
Hi,
I don't remember very many of the identities in trigonometry, but two
I do remember are
 sin(A + B) = sin(A)cos(B) + cos(A)sin(B), and
 sin^{2}(A) + cos^{2}(A) = 1
So what I see is that if your professor had said
write sin 2x in terms of sin x Then you could use identity 1. above
to get sin(2x) = sin(x)cos(x) + cos(x)sin(x) = 2 sin(x)cos(x) This
is not quite correct since I have cos(2x) in terms of sin(x) and cos(x).
But identity 2. above says that cos(x) = sqrt(1  sin^{2}(x))
where sqrt is the square root. Thus sin(2x) = 2 sin(x) sqrt(1sin^{2}(x))
To answer your professor's question about sin(3x) first
write sin(3x) = sin(x + 2x)
Now use 1. above to write this in terms of
sin(x) and sin(2x). But from what I did above you can write sin(2x) in terms
of sin(x).
Cheers,
Penny 
