William W. answered • 06/07/19
Experienced Tutor and Retired Engineer
The generic function for cosine is Acos(B(x - C)) + D where A is the amplitude (the number up and down from the central axis) and B is the number that defines the period. It’s not the period itself though. To find the period you take the normal period of cosine, which is 2π and divide it by B, in other words Period = 2π/B. Since we are looking for the number B to put in the equation, we can say 7 = 2π/B or B = 2π/7. The A in this case is 7. The other numbers C and D are not used in this case. C is the shift in the x-direction (horizontal shift aka phase shift) and D is the vertical shift.
So, the equation is f(x) = 7cos[(2π/7)x]
