Determine the number of cycles the following sine function has in the interval from 0 to 2π. Find the amplitude and period of the function.
y = -8sinπ0
show your work/steps
The given sine function is y = -8sin(πx).
To find the number of cycles in the interval from 0 to 2π, we need to determine how many complete wave patterns occur in this interval.
The general form of a sine function is y = A*sin(Bx + C), where A represents the amplitude, B represents the period, and C represents any phase shift. In this case, we have y = -8sin(πx).
Comparing this to the general form, we can see that the amplitude is A = -8.
To find the period, we need to solve the equation Bx = 2π to find the value of B that completes one full cycle within the interval from 0 to 2π. In this case, B = π.
Now, we can find the number of cycles by dividing the interval length (2π) by the period (π):
Number of cycles = (2π) / π = 2
Therefore, the given sine function has 2 complete cycles in the interval from 0 to 2π.
The amplitude of the function is -8, and the period is π.