
Philip P. answered 05/01/17
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The general form for a cosine (or other trig function) function is:
f(x) = a·cos(b(x-c)) + d
Where:
- a = amplitude
- b = 2pi/period, so period = 2pi/b
- c = horizontal or phase shift
- d = vertical shift
First, we must put your function into that form:
f(x) = −5·cos(4πx−12π) + 3
f(x) = −5·cos(4π(x−3)) + 3
- a = amplitude = -5
- b = 4pi = 2pi/period; so period = 2pi/4pi = 1/2
- c = phase shift = 3
- d = vertical shift = 3