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

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Answer 1 · 2018-04-08T03:36:56

#x= 1/6+-2n, 5/6+-2n# where #n ∈ Z#

#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]}