# How to evaluate $-\pi \sin(\pi)+\cos(\pi)$ without a calculator?

Hi I'm doing derivatives of trigonometric functions. I needed to find the value of the derivative at $$x=\pi,$$ where $$\frac{dy}{dx} = -x\sin x +\cos x.$$ I found that this was -1 using the calculator, however is this possible to do without a calculator? How does the calculator evaluate this?

I haven't studied advanced trig as of yet.

Thanks

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You know that $\sin \pi=0$, right? And that $\cos\pi=-1$? –  Henning Makholm Aug 29 '13 at 13:14
Frankly, if you don't know $\sin\pi$ and $\cos\pi$ without using a calculator, studying derivatives feels kinda pointless. –  Jyrki Lahtonen Aug 29 '13 at 13:16
@HenningMakholm i didn't think of that, thanks –  salman Aug 29 '13 at 13:20

Since $\sin\pi = 0$ and $\cos\pi = -1$, $$-x\sin x + \cos x = -\pi \sin \pi + \cos\pi = -\pi\cdot 0 + (-1) = -1.$$