What is the function of cos that has an amplitude of 4, a period of 2π, and has a point at (0,2)
mmmhhh, how about
y = 4 cos x to start with
when x = 0 , y would be 4, but we need it to be 2, so
y = 4cos x - 1
https://www.wolframalpha.com/input/?i=graph+y+%3D+4cos+x+-+1
To understand the function of cosine (cos), let's break down the given information:
1. Amplitude: The amplitude of a cosine function represents half the distance between the maximum and minimum values. In this case, the amplitude is 4, indicating that the maximum value would be 4 and the minimum value would be -4.
2. Period: The period of a cosine function is the distance between corresponding points in one cycle. In this case, the period is given as 2π, which means that one complete cycle of the cosine function occurs over an interval of 2π.
3. Point: The given point (0,2) represents a specific coordinate on the graph of the cosine function. The x-coordinate of 0 indicates that the function reaches its maximum value at this point, while the y-coordinate of 2 signifies that the maximum value is 2.
Based on this information, we can form the equation for the cosine function:
f(x) = A * cos(Bx) + C
where:
- A represents the amplitude
- B determines the frequency, which is the reciprocal of the period (B = 2π/period)
- C is the vertical shift (C represents the value added to or subtracted from the function)
For this particular function, the equation can be written as:
f(x) = 4 * cos((2π/2π)x) + 2
Simplifying further:
f(x) = 4 * cos(x) + 2
Therefore, the function of cosine with an amplitude of 4, a period of 2π, and a point at (0,2) is given by f(x) = 4 * cos(x) + 2.