How do you find the amplitude, phase shift and period of #y=2/3 sin πx#?

1 Answer
Jul 24, 2015

The general formula for #sinx# is:

#y = Asin(kx + phi) + h#
where:
#A# is amplitude
#k prop 1/T#, i.e. if #k = 1#, then #T = 2pi#, but if #k = 2#, then the period is #pi#
#phi# is the phase shift left or right (left is positive, right is negative)
#h# is the vertical shift (up is positive, down is negative)

From this you should be able to identify that:

#A = 2/3#
#k = pi#
#phi = 0#
#h = 0#

Thus, with #k = pi#,
#pi*1/T = 1/(2pi)*pi = 1/2 -> T = 2 "rad"#