# Answer on Algebra Question for Brandy

Question #6307

Write an equation of the cosine function with amplitude 2 and period 8π.

Expert's answer

f(x)=2cos(x/4)

Let's verify if written function meets the requirements:

|2cos(x/4)|<=2& -amplitude

f(x+8pi)=2cos((x+8pi)/4)=2cos(x/4+2pi)=2cos(x/4)=f(x) - so 8pi is the period

Let's verify if written function meets the requirements:

|2cos(x/4)|<=2& -amplitude

f(x+8pi)=2cos((x+8pi)/4)=2cos(x/4+2pi)=2cos(x/4)=f(x) - so 8pi is the period

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