Find the (trigonometric) limit

• October 14th 2009, 07:42 PM
s3a
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!
• October 14th 2009, 07:48 PM
alexmahone
Quote:

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!

$\lim_{t\rightarrow 0} \frac{\tan (6t)}{\sin (2t)}=\lim_{t\rightarrow 0} \frac{\tan (6t)}{6}\frac{2}{\sin(2t)}\frac{6}{2}=1*1*3=3$
• October 14th 2009, 07:52 PM
matt.qmar
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.