Find all real numbers to satisfy equation? sin(πx)=1/2

1 Answer
Apr 8, 2018

x= 1/6+-2n, 5/6+-2n where n ∈ Z

Explanation:

sin(pix)=1/2

Let pix be u:
sin(u)= 1/2

u= pi/6+-2pin, (5pi)/6+-2pin

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

pix= pi/6+-2pin, (5pi)/6+-2pin

x= 1/6+-2n, 5/6+-2n where n ∈ Z

graph{sin(pix)-1/2 [-10, 10, -5, 5]}