Find all real numbers to satisfy equation? 2sin(x/2)-1=0

1 Answer
Apr 8, 2018

#x= pi/3+-4pin, (5pi)/3+-4pin# where #n ∈ Z#

Explanation:

#2sin(x/2)-1=0#

Let #x/2# be #u#:
#2sin(u)-1=0#
#sin(u)= 1/2#

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

Now replace #u# with #x/2# and solve for #x# by multiplying by #2#:

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

#x= pi/3+-4pin, (5pi)/3+-4pin# where #n ∈ Z#

graph{2sin(x/2)-1 [-3.04, 16.96, -5.08, 4.92]}