# Math Help - Find the (trigonometric) limit

1. ## Find the (trigonometric) limit

How do I find the following limit?:

lim t --> 0 (tan 6t)/(sin 2t)

(The answer is 3 and I could also figure that out by plugging in t = 0.01 but I would like to know the legitimate way of doing this. My teacher taught us similar stuff but I don't think he went over this particular type of problem)

Any help would be greatly appreciated!
Thanks in advance!

2. Originally Posted by s3a
How do I find the following limit?:

lim t --> 0 (tan 6t)/(sin 2t)

(The answer is 3 and I could also figure that out by plugging in t = 0.01 but I would like to know the legitimate way of doing this. My teacher taught us similar stuff but I don't think he went over this particular type of problem)

Any help would be greatly appreciated!
Thanks in advance!
$\lim_{t\rightarrow 0} \frac{\tan (6t)}{\sin (2t)}=\lim_{t\rightarrow 0} \frac{\tan (6t)}{6}\frac{2}{\sin(2t)}\frac{6}{2}=1*1*3=3$

3. note tan(6t)= sin(6t)/cos(6t).
lim t->0 of cos6t=cos0=1
multiply by (2t*3)/6t, then split the limits to
sin(6t)/6t and sin(2t)/2t. you're left with two limits going to 1, a cos0=1 and and 3, so the limit is 3.