What is the period and amplitude of `f(x) = -2cos(3x-pi/2)-4 ` ?

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lemjay's profile pic

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

When a cosine function is in the form `f(x) = Acos(Bx - C)+ D` , its period is `2pi/|B|` . And, its amplitude is `|A|` .

So to determine the period of `f(x)=-2cos(3x-pi/2)-4` , plug-in B=3x to the formula.

Period`=(2pi)/B=(2pi)/3`

And, to get the amplitude, plug-in A=-2.

Amplitude`=|A|=|-2|=2`

Hence, the period of the given cosine function is `(2pi)/3`  and its amplitude is 2 units.

rachellopez's profile pic

rachellopez | Student, Grade 12 | (Level 1) Valedictorian

Posted on

Amplitude is equal to the coefficient in front of the cos. In this case your amplitude is 2. It isn't negative because the amplitude measures distance, which can't be negative. 

The period is equal to 2pi divided by the coefficient in front of x. That means that 2pi/3 would be the period. 

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