Find the limit of the function

find the limit as t approaches 0 for the function (tan3t)/(sin4t)

please tell me how i should solve problems like this when there are trig functions involved

lim t→0 tan(3t) / sin(4t)

You know that
lim x→0 sin(ax)/(ax) = 1, for a ≠ 0, right?

Likewise,
lim x→0 (ax)/sin(ax) = 1, for a ≠ 0. (It's just the reciprocal of the previous limit.)

Also, recall
tan(3t) = sin(3t) / cos(3t)

lim t→0 (sin(3t) / cos(3t)) / sin(4t)
lim t→0 (4t ∙ 3t)/(4t ∙ 3t) ∙ (sin(3t) / cos(3t)) / sin(4t)
lim t→0 (4t)/sin(4t) ∙ sin(3t)/(3t) ∙ (3t)/(4t cos(3t))
[lim t→0 (4t)/sin(4t)] ∙ [lim t→0 sin(3t)/(3t)] ∙ [lim t→0 (3t)/(4t cos(3t))]
1 ∙ 1 ∙ (3/4) [lim t→0 1/cos(3t)]
3/4 (1/1)
3/4