#y=sin(theta)# has an amplitude of #1#

#color(white)("XXXX")##y# varies between #+1# and #-1#

If #y=4sin(theta)#

#color(white)("XXXX")#then #y# will vary between #+4# and #-4#

#color(white)("XXXX")##rarr y=4sin(theta)# has an amplitude of #4# (for any #theta#)

#y=k*sin(theta)# has a period of #2pi#

#color(white)("XXXX")##y# completes one cycle while #theta# increases by #2pi#

if #3x =theta#

#color(white)("XXXX")##y# completes one cycle while #3x# increases by #2pi#

#color(white)("XXXX")#or (expressed in another way)

#color(white)("XXXX")##y# completes #1/3# of a cycle while #x# increase by #2pi#

#color(white)("XXXX")##rArr y# completes 1 cycle while #x# increases by #3xx2pi = 6pi#