# Find all real numbers to satisfy equation? Cos(2πx)=0

Apr 8, 2018

$x = \frac{1}{4} \pm n , \frac{3}{4} \pm n$ where n ∈ Z

#### Explanation:

$\cos \left(2 \pi x\right) = 0$

Let $2 \pi x$ be $u$:
$\cos \left(u\right) = 0$

$u = \frac{\pi}{2} \pm 2 \pi n , \frac{3 \pi}{2} \pm 2 \pi n$

Now replace $u$ with $2 \pi x$ and solve for $x$ by dividing by $2 \pi$:

$2 \pi x = \frac{\pi}{2} \pm 2 \pi n , \frac{3 \pi}{2} \pm 2 \pi n$

$x = \frac{1}{4} \pm n , \frac{3}{4} \pm n$ where n ∈ Z

graph{cos(2pix) [-10, 10, -5, 5]}