1. ## Limit w/trig functions

I can do everything that we have covered in class so far except for problems involving trig functions! The ones that bother me the most are when I'm supposed to find the limit when I have something like f(x)=csc(x) and x is approaching pi/2 from the right... Does anyone know of an online tutorial that could help me out with trig functions when finding limits?

I'm doing the chapter review right now for a test tomorrow, and I am currently stumped with this problem:

lim x-->0 tan(2x)/tan(pi*x)

I thought that because I plugged in x and therefore got tan(0)/tan(0), that the limit would be 1. Apparently it is 2/pi. How did that work out?!

2. Originally Posted by tom ato
I can do everything that we have covered in class so far except for problems involving trig functions! The ones that bother me the most are when I'm supposed to find the limit when I have something like f(x)=csc(x) and x is approaching pi/2 from the right... Does anyone know of an online tutorial that could help me out with trig functions when finding limits?

I'm doing the chapter review right now for a test tomorrow, and I am currently stumped with this problem:

lim x-->0 tan(2x)/tan(pi*x)

I thought that because I plugged in x and therefore got tan(0)/tan(0), that the limit would be 1. Apparently it is 2/pi. How did that work out?!

tan(2x)/tan(pi*x)= [sin(2x).cos(pi*x)]/[cos(2x).sin(pi*x)]....................1

But sin(2x)= $2x.\frac{\ sin(2x)}{ 2x}$.................................................. ......................................2

Also sin(pi*x)= $\pi x.\frac{\ sin(\pi x)}{\pi x}$.................................................. .......................................3

Substitute now (2) and (3) into (1) and now let x go to zero we get:

.................................................2/pi................................................

Because:

$\lim_{ A to 0}{\frac{\ sin(A)}{ A}}$ =1.

And cos(0)=1

3. I am sorry i forgot to write that tan(0)/tan(0) = 0/0 ,which is undefined ,and not equal to 1