Question

limit of function sin(휃)/휃 as 휃->0 (휃 is in degrees)

Answer 1

\[\lim_{\theta \rightarrow 0} \sin \theta/ \theta\]

Theta being in degrees. I need the proof to understand it better.

Answer 2

any ideas?

Answer 3

that is one cool looking theta!

Answer 4

haha, yea. its got attitude

Answer 5

are you good with limits satellite73?

Answer 6

it is true that \(\lim_{x\to 0}\frac{\sin(x)}{x}=1\) but not true if you are working in degrees.
to compute this limit, convert from degrees to radians and then you can use l'hopital

Answer 7

ok, let me work it out...

Answer 8

oops sorry, denominator is still \(x\) i made a mistake there

Answer 9

i thought you had to do top and bottom?

Answer 10

it should be
\[\lim_{x\to 0}\frac{\sin(\frac{\pi x}{180})}{x}\]

Answer 11

ok saying "x is in degrees" means you are thinking of the function sine as a function of angles measured in degrees. but also \(x\) is a real number. so to compute this limit you use the sine function as a composition of functions, i.e. you convert it to a function of degree by making it \(\sin(\frac{\pi x}{180})\) and now your function is measuring in degrees. but \(x\) is still going to zero

Answer 12

btw this is a great problem, because it shows you that the derivative of sine is NOT cosine if you are thinking of these functions as functions of degrees

Answer 13

I see... I think i can solve it from here. Im sure that is why it was one of the problems assigned in my class, we're just touching on this subject.

Thank you for your help!

Answer 14

yw
use l'hopital and chain rule