write a cosine function

Question

Write a cosine function that has a midline of 4, an amplitude of 2 and a period of 7π/5

Answer 1

y = 2Cos[(10/7)x] + 4

In general, y = aCosb(x-c) + d

a = amplitude = 2

b = 2pi/period = 2pi/(7pi/5) = 10/7

c = phase shift = 0

d = vertical shift = 4

Note that the high will be 6 and the low will be 2.

Answer 2

The generic cosine function can be written as:

where "A" is the amplitude, "B" defines the period where the period is 2π/B, "C" is the horizontal shift or phase shift, and "D" is the vertical shift or midline location.

We can just plug in A = 2 and D = 4 but we need to calculate "B". since the period is 2π/B then B = 2π/period so B = 2π/(7π/5) = 2π•5/(7π) = 10π/7π = 10/7

In this case C = 0