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What is the amplitude and period of f(t)=2.5tan(t)

A. amplitude: 2.5; period: π
B. amplitude: 2.5; period: 2π
C. amplitude: none; period: 2π
D. amplitude: none; period: π

I selected A, and I do not know why I got it wrong.

User Canacourse
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1 Answer

4 votes

Answer:

D

Explanation:

Tan graphs are a bit different to sin and cos graphs: they don't have an amplitude.

If you look at a tan graph, it exists between assymptotes and has no maximum or minimum value. In this case, the 2.5 acts similar to a dilation factor and makes the graph skinnier or wider.

You were right about the period: it is just pi, not 2 pi like sin and cos. Again, if you look at the graph, the assymptotes occur every period, which is only pi.

Hope that helped : )

User Aditya Manohar
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3.8k points