How do you find the amplitude, period, and shift for #y = -sin(x-3π/4)#?

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Answer 1 · 2016-10-11T14:20:29

A = -1
#tau = 2pi#
#theta = -(3pi)/4#

The general form for a sine wave is:

#y = Asin(Bx + C) + D#

A is the amplitude
B is a number that contains the frequency, #f#, and the period, #tau#

#B = 2pif#
#f = B/(2pi)#

Because the #f = 1/tau#, the following is, also, true:

#B = (2pi)/tau#
#tau = (2pi)/B#

C is a number that contains the phase shift, #theta#:

#theta = C/B#

D is the vertical shift

Given:

#y = -sin(x - (3pi)/4)#

The amplitude:

A = -1

The period:

#tau = (2pi)/1 #
#tau = 2pi#

The phase shift:

#theta = -(3pi)/4#