Question

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

Answer 1

`x= 1/4+-n, 3/4+-n` where `n ∈ Z`

Explanation:

`cos(2pix)=0`

Let `2pix` be `u`:
`cos(u)= 0`

`u= pi/2+-2pin, (3pi)/2+-2pin`

Now replace `u` with `2pix` and solve for `x` by dividing by `2pi`:

`2pix= pi/2+-2pin, (3pi)/2+-2pin`

`x= 1/4+-n, 3/4+-n` where `n ∈ Z`

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