How do you find the amplitude, period and phase shift for #y=cos3(theta-pi)-4#?

1 Answer
Oliver S.
Mar 30, 2018

See below:

Explanation:

Sine and Cosine functions have the general form of

#f(x)=aCosb(x-c)+d#

Where #a# gives the amplitude, #b# is involved with the period, #c# gives the horizontal translation (which I assume is phase shift) and #d# gives the vertical translation of the function.

In this case, the amplitude of the function is still 1 as we have no number before #cos#.

The period is not directly given by #b# , rather it is given by the equation:
Period#=((2pi)/b)#
Note- in the case of #tan# functions you use #pi# instead of #2pi#.

#b=3# in this case, so the period is #(2pi)/3#

and #c=3 times pi# so your phase shift is #3pi# units shifted to the left.

Also as #d=-4# this is the principal axis of the function, i.e the function revolves around #y=-4#

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