limits question. dont know how to start

Using l'Hopitals rule

lim     sin  θ  =    0

θ → 0   

First, we can rewrite the numerator:

lim theta -> 0 (1 - cos theta)/theta = lim theta -> 0 2 sin(theta/2)^2/theta

We can then simplify and apply l'Hopital's Rule:

lim theta -> 0 2 sin(theta/2)^2/theta = lim theta ->0  4 sin (theta/2) cos(theta/2)/1 = 4.

Therefore, the limit is 4.