I made graphs and th enext step is to create equations...
Write the equation of each cycle in the form y=sin(bx+c). What is the Period and Phase Shift for the ophysical, emotional, and intellectual cycles? Feb. 13th, 2015 is at the origin.
I dont' exactly get what a period is and where you get the b and c values.
Any help would be appreciated, Thanks in advance :)
To write the equation of each cycle in the form y = sin(bx + c), you need to understand the concepts of period and phase shift.
1. Period: The period of a sinusoidal function is the length of one complete cycle. It represents the distance it takes for the function to repeat itself. In the case of sin(bx + c), the period is found using the formula:
Period = 2π / |b|
The |b| is the absolute value of b, the coefficient in front of x. For example, if b = 2, the period would be 2π / 2 = π.
2. Phase Shift: The phase shift is the horizontal shift of the graph. It tells you where the sinusoidal function starts its cycle. The phase shift in sin(bx + c) is given by:
Phase Shift = -c / b
If c is positive, it means the graph is shifted to the left; if c is negative, it is shifted to the right.
Now, to find the equations and values for the ophysical, emotional, and intellectual cycles, you need some additional information. Specifically, you need to know the periods and phase shifts of each cycle.
Since Feb. 13th, 2015, is at the origin, the phase shift for all cycles will be zero. This means the cycles will start from the origin.
To find the periods, you need to determine the length of each complete cycle by identifying the dates when the cycles repeat. For example, if the emotional cycle repeats every 28 days, the period would be 28 days.
Once you have the periods and phase shifts, you can write the equations in the form y = sin(bx + c) using the given values of b (2π / period) and c (0 for each cycle since they start from the origin).
I hope this explanation helps you understand how to proceed with finding the equations of the cycles. If you have specific information about the periods and phase shifts, I can guide you in writing the equations.