cosine function

Question

Write a cosine function that has an amplitude of 4, a midline of 2 and a period of 3π/4

Answer 1

Answer: f(x) = 4cos(8x/3) + 2

Method:

1. A general cosine function is f(x) = Acos(wx), where A is amplitude, w is frequency, and x is position.
2. w = 2πf = 2π/T . So w = 2pi/(3pi/4) = 8/3
3. f(x) = 4cos(8x/3) would satisfy this problem but now we need to worry about midline
4. Since you need a midline of 2 and not 0, it cannot be a normal cosine function that propagates with a midline on the x-axis, it needs to be pushed up somehow. This can be accomplished by shifting everything two units up.
5. f(x) = 4cos(8x/3) + 2

Let me know if you have any questions!