Question

limx→0 sin x/x
I understand that this is 1 when we are talking about radians... but the question says x is measured in degrees... What do?

Answer 1

This doesn't make any difference, because you change a quantity x given in degrees into radians by multiplying with a constant C, where
\[ C = \frac{360^\circ}{2\pi} \]
Notice that when x goes to zero, C*x still goes to zero.
So this is nothing but scaling your quantity.

Answer 2

Try substituting C*x for x and compute with L'Hopitals rule. You will see that by the chain rule, the constant drops out.

Answer 3

= limit dsinx dx = cos x
--------
dx/dx
lmt >0 of cos x = 1

Answer 4

\[ \lim_{x\rightarrow 0} \frac{\sin(C x)}{Cx} = \lim_{x\rightarrow 0} \frac{C\cos(Cx)}{C} = \frac{C}{C}\cdot \cos(C\cdot 0) = \cos(0) = 1 \]

Answer 5

\[\frac{\pi}{180}\]

Answer 6

Thanks again guys.

Answer 7

Just to make sure...the answer is not 1. it is \[\frac{\pi}{180}\]