Determine the number of cycles the following sine function has in the interval from 0 to 2π. Find the amplitude, sine function and period of the function.
y = -8sinπ0
show your work/steps
The given function is y = -8sin(πx).
To determine the number of cycles in the interval from 0 to 2π, we need to find the number of times the function completes a full oscillation within that interval.
Since the coefficient of x in the sine function is π, the period of the function is given by the formula T = 2π/π = 2.
Therefore, the function completes one full cycle (oscillation) within each interval of length 2.
So in the interval from 0 to 2π, the function completes one cycle.
The amplitude of the function is the absolute value of the coefficient multiplying the sine function, which in this case is 8. Therefore, the amplitude is 8.
The sine function can be represented as y = A sin(Bx), where A is the amplitude and B determines the period.
So, the sine function for the given equation of y = -8sin(πx) is y = 8sin(πx), since the negative sign is already in front of the sine function.
To summarize:
- Number of cycles in the interval from 0 to 2π: 1 cycle
- Amplitude: 8
- Sine function: y = 8sin(πx)
- Period: 2