Question

I have a question about radians vs degrees when determining a limit.

Answer 1

I'm working on the following limit:
\[\lim_{x \rightarrow \pi} (\sin x/-\sin x)\]
I realize that this = 0, and that I need to use l'hopital's rule. My question is much simpler.

This = -1 if I'm using degrees, but the correct answer of 0 (0/0) if I'm using radians.
Would someone explain to me why I should be using radians?

Answer 2

yes because Pi is referring to the unit circle.
The Sin graph itself is in Radians, because Radians are always written with Pi

Answer 3

I mean if you're dealing with Pi in trig, its a Radians problem

Answer 4

Are you sure the right answer is 0?

Answer 5

it can't be

Answer 6

also \[0\neq\frac00\]

Answer 7

Hermeezey, perfect, thanks. That's the kind of thing I was looking for. So essentially, if I see a problem using pi, I need to be thinking radians, right?

PaxPolaris, yeah, the problem comes with an answer. Because it comes out to 0/0, I need to find the derivative. So the ultimate answer isn't 0, but because the problem I listed comes out to 0, I need to take it further.

Ah, TuringTest, I guess you're right. Infinity then?

Answer 8

\[\frac00\]is what is called an indeterminate form. That means it's just not defined, as apposed to plus or minus infinity.

Answer 9

In fact you can only use l'hospital's rule if by plugging in the value you are approaching you get one of the following indeterminate forms:\[\frac00\text{ or }\frac{\pm\infty}0\text{ or }\frac0{\pm\infty}\]if you had something that evaluated to\[\pm\infty\]for instance, using l'hospital is against the rules

Answer 10

Great. You're answering questions I didn't even know I had. :) Thanks all!

Answer 11

anytime :D

Answer 12

Nice, TuringTest. Thanks.

Answer 13

\[\Large let\ f(x)= { \sin(x)\over -\sin(x) }\]
\[{\Large \therefore f(x) =-{\cancel {\sin(x)}\over \cancel {\sin(x)}}= -1} ....except\ when\ \sin(x)\ is\ 0 \ where\ it\ is\ undefined\] as you cannot divide by 0

while f(π) is undefined,\[\Huge \lim_{x \rightarrow \pi}f(x)=-1\]