# How do you find the intersections points of y=2cos(2pix) and y=-2sin(pix)?

Sep 23, 2016

$x = \frac{1}{2} + 2 k$ with $k = 0 , \pm 1 , \pm 2 , \cdots$

#### Explanation:

The intersection points are the points in which

$2 \cos \left(2 \pi x\right) = - 2 \sin \left(\pi x\right)$ or
$\cos \left(2 \pi x\right) = - \sin \left(\pi x\right) = \cos \left(\pi x + \frac{\pi}{2}\right)$

so

$2 \pi x = \pi x + \frac{\pi}{2} + 2 k \pi$ or

$x = \frac{\frac{\pi}{2} + 2 k \pi}{\pi} = \frac{1}{2} + 2 k$ with $k = 0 , \pm 1 , \pm 2 , \cdots$