Question

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

Answer 1

`x = 1/2+2k` with `k = 0, pm1,pm2,cdots`

Explanation:

The intersection points are the points in which

`2cos(2pix)=-2sin(pix)` or
`cos(2pix)=-sin(pix) = cos(pi x+pi/2)`

so

`2pix=pix+pi/2+2kpi` or

`x = (pi/2+2kpi)/pi = 1/2+2k` with `k = 0, pm1,pm2,cdots`