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

1 Answer
Apr 8, 2018

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]}