How do you find the amplitude, period, and shift for #y =3cos(6x+8pi)#?

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Answer 1 · 2016-03-23T02:17:54

See solution below.

Amplitude:

In a function of the form #y = acosb(x + c) + d#, the amplitude is #| a |#. Therefore, your amplitude is of 3.

Phase shift:

The phase shift can be found by setting the numbers in parentheses to 0.

#6x + 8pi = 0#

#6x = -8pi#

#x = (-4pi)/3#

Therefore, the phase shift is #(4pi)/3# units left.

Period:

The formula for period in sine and cosine functions is #P = (2pi)/b#, where P is the period and b is term b in your equation.

In your equation, we're going to have to factor b out.

#y = 3cos(6x + 8pi) -> y = 3cos2(3x + 4pi) -> b = 2#

#P = (2pi)/2#

#P = pi#

Here is the graph of your function:

Grapher

Practice exercises:

Identify the period, phase shift and amplitude of #y = -4cos(2x - pi/2)#. Graph if possible.

Good luck!