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]}