Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.


share|cite|improve this question
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
up vote 6 down vote accepted

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

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.