Applications of Identities

sin 5x  = 1/2

Note that the "5" "horizontally compresses" the normal sine curve by a factor of 5

So......for sin (x), there will 2 solutions on (0, 2pi) where sin x = 1/2

So....2 values in one normal period

But....we have 5 periods  on (0, 2pi)  for sin (5x)

So.....there will be  5(2)  =  10  solutions  for  sin (5x)  = 1/2