algebra precalculus - calculate angle when delta x = 0,001

I'm busy with a homework assignment (differentiating), and I don't understand it because the book has no explanation given. In the book it says:

"Show that when your calculator is on the setting RAD(radians) and $\Delta x = 0.001$, that the angle of the slope of $O(0,0)$ to $y=\sin x$ is about 45°"

I don't know how to put my calculator on the RAD setting.

What I tried was $\tan^{-1}(\frac{\sin 0.001}{0.001})$, because $\frac{\Delta y}{\Delta x}$ is how u calculate the slope, and I thought that when u get the inverse tangent of the slope you get the angle.
I don't get 45° as my answer when I tick it into my calculator.

What am I doing wrong?

Please don't use symbols in your answers, I hardly know any.

Can someone edit my question into LaTeX?

Edit:

How come the arctan of 1 on my calculator doesn't return 45 but 0.7853...

Edit 2:

When I put it back on degrees mode and I take the arctan of 1 it returns 45. My question is solved, but can someone explain why the arctan is different in radians mode?

More importantly can someone explain why I need to put it on radians mode?

Answer

If you compute $\frac{\sin 0.001}{0.001}$ on your calculator, you should get $\approx 1$. $\arctan$ of that is $45$ degrees or $\frac{\pi}{4}$ in radians.