# Thread: Limits of trig functions

1. ## Limits of trig functions

Can someone help me with the following questions:

1) [1-cos2x]/[x^2] as x approaches 0
2) [cotx]/[pi/2 - x] as x approaches pi/2
3) [sin]/[x-pi] as x approaches pi

I know that 1-cosx/x^2 is 1/2, but I don't know how this could be used when it's cos2x. I'm not really sure how I could approach the second or third questions. Could I get some advice?

2. Try some trig identities

$\lim_{x \to 0}\frac{1-\cos(2x)}{x^2}=\lim_{x \to 0}\frac{2\sin^{2}(x)}{x^2}=2$

3. Originally Posted by theowne
Can someone help me with the following questions:

1) [1-cos2x]/[x^2] as x approaches 0
2) [cotx]/[pi/2 - x] as x approaches pi/2
3) [sin]/[x-pi] as x approaches pi

I know that 1-cosx/x^2 is 1/2, but I don't know how this could be used when it's cos2x. I'm not really sure how I could approach the second or third questions. Could I get some advice?
for 3 let $u=x - \pi$

$\lim_{x \to \pi}\frac{\sin(x)}{x-\pi}=\lim_{u \to 0}\frac{\sin(u + \pi)}{u}$

Now use the sum identity for sine

Try the same thing on #2.

Good luck.