# Math Help - Trig Limit #2

1. ## Trig Limit #2

Another one that I can 't get:

$\displaystyle \lim_{t\to 0 } \frac {sin^2 3t}{t^2}$

Can I convert this to:

$9 * \displaystyle \lim_{t\to 0 } \frac {sin^2 t}{t^2}$

If so, then the solution seems easy ( $9 * 1 = 9$)

But I suspect that my algebra is faulty.

Thanks.

2. Originally Posted by reastland
Another one that I can 't get:

$\displaystyle \lim_{t\to 0 } \frac {sin^2 3t}{t^2}$

Can I convert this to:

$9 * \displaystyle \lim_{t\to 0 } \frac {sin^2 t}{t^2}$

If so, then the solution seems easy ( $9 * 1 = 9$)

But I suspect that my algebra is faulty.

Thanks.
What? How did you get that 9?

3. $(3t)^2 = 9t^2$

I knew that it was wrong. The answer to the question is 9, so I backed into the idea that you could extract the $3^2$, but I didn't like it. I think that I'll try $\sin{(2t + t)}$ unless you think that is the wrong direction.

4. $\displaystyle \frac{\sin^2{3t}}{t^2} = \frac{9\sin^2{3t}}{9t^2}$

$\displaystyle = 9\left(\frac{\sin{3t}}{3t}\right)^2$.

This should now be easy to evalute.

5. Originally Posted by reastland
$(3t)^2 = 9t^2$

I knew that it was wrong. The answer to the question is 9, so I backed into the idea that you could extract the $3^2$, but I didn't like it. I think that I'll try $\sin{(2t + t)}$ unless you think that is the wrong direction.
You can't just pull it out like that.

6. That looks more like the format I was aiming for. Thanks!