How do i find the phase shift in this problem

Naturalists find that the populations fo some kinds of predatory animals vary periodically. Assume that the population of foxes in a certain forest varies sinusoidally with time. Records started being kept when time t = 0 years. A minimum number, 200 foxes, occurred when t = 2.9 years. The next maximum, 800 foxes, occurred at t = 5.1 years.

The time from a minimum to a maximum is 1/2 the period.

So I do I find the phase shift based off this?

To find the phase shift in this problem, we need to determine the difference between the time when the sinusoidal function reaches its maximum or minimum and the time when the function starts. The phase shift is the horizontal shift of the graph of the sinusoidal function.

In this problem, the minimum number of foxes occurred when t = 2.9 years, and the next maximum occurred at t = 5.1 years. The difference between these two times gives us the period of the sinusoidal function. The period is the length of one complete cycle of the function.

Here's how to find the phase shift step by step:

1. Calculate the period: The period is the difference between the two times when the function reaches its maximum or minimum. In this case, the period is 5.1 years - 2.9 years = 2.2 years.

2. Divide the period by 4: Since the sinusoidal function is assumed to be a standard sine or cosine function, one complete cycle corresponds to 2π radians or 360 degrees. In our case, we need to divide the period by 4 to find the phase shift. So, 2.2 years / 4 = 0.55 years.

3. Convert years to radians or degrees: To find the phase shift, we need to convert the time interval, which is in years, to radians or degrees. Since one complete cycle is 2π radians or 360 degrees, we can use this conversion factor.

4. Calculate the phase shift: Multiply the time interval in years by the conversion factor to obtain the phase shift. In our case, the phase shift is 0.55 years * (2π radians / 2.2 years) = approximately 3 radians.

Therefore, the phase shift in this problem is approximately 3 radians.