Reducing fractions with pi in them

I am trying to simplify the expression

$\displaystyle \cos\frac{35\pi}{4}+i\sin\frac{35\pi}{4}$

The cosine and sine functions can be reduced modulo $\displaystyle 2\pi$, right? So I wrote this as

$\displaystyle \cos\frac{3\pi}{4}+i\sin\frac{3\pi}{4}$

after subtracting $\displaystyle \frac{32\pi}{4}=8\pi$ from each of the arguments. But checking this equality with my calculator I get something different. What am I doing wrong?

Re: Reducing fractions with pi in them

Maybe something's wrong with your calculator settings. I get $\displaystyle cos\left(\frac{35\pi}{4}\right) = cos\left(\frac{3\pi}{4}\right) = -\frac{\sqrt{2}}{2}$ and $\displaystyle sin\left(\frac{35\pi}{4}\right) = sin\left(\frac{3\pi}{4}\right) = \frac{\sqrt{2}}{2}$

Re: Reducing fractions with pi in them

A common mistake might be at play. Make sure you are in 'radian' mode.

-Dan

Re: Reducing fractions with pi in them

Ah, I should have known! Thanks!