How do you solve $\cos \pi z =0$?

Question

How do you solve $\cos \pi z =0$? I am unsure what to do with the $\pi$. I know how to solve $\cos z = 0$, but $\pi$ is throwing me off. Can someone help start me off with this question please?

You could try the substitution $y = \pi z$? Once you know $y$, just divide it by $\pi$ — graydad, May 14 '15 at 14:03

score 3 · Answer 1 · answered May 14 '15 at 14:03

3

$\cos(\pi z)=0$

$\pi z=(2k+1)\frac{\pi}{2}$

$z=\frac{2k+1}{2}$ where $k$ is an integer.

answered May 14 '15 at 14:03

Hasan Saad

4,545

score 0 · Answer 2 · answered May 14 '15 at 14:08

0

Sounds like you already have the answer. If you can and have solved $$\cos(z)$$ then you have found $z$. Just divide this $z$ by $\pi$ and it will give you the solution.

answered May 14 '15 at 14:08

graydad

14,077

score 0 · Answer 3 · answered May 14 '15 at 16:16

0

$$\cos(\pi z)=0<=>$$ $$\pi z=\cos^{-1}(0)<=>$$ $$\pi z=\frac{\pi}{2}+\pi n<=>$$ $$z=n+\frac{1}{2}$$

(with n is the element of Z -> the set of integers)

answered May 14 '15 at 16:16

Jan Eerland

28,671

How do you solve $\cos \pi z =0$?

3 Answers3