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 = -2sin2π0
show your work/steps
The given function is y = -2sin(2π0)
To determine the number of cycles in the interval from 0 to 2π, we need to find the range of x values in which the sine function completes one full cycle.
The general form of a sine function is y = A*sin(Bx + C), where A is the amplitude, B determines the period, and C is a phase shift. In this case, C = 0.
Comparing the given function to the general form, we can see that A = -2 and B = 2π.
The amplitude, denoted as |A|, is the absolute value of A. Therefore, the amplitude of this function is 2.
The period of a sine function is given by the formula T = 2π/B. Plugging in the value of B, we get T = 2π/(2π) = 1.
Since the interval from 0 to 2π is exactly one period, the function completes one full cycle in this interval.
Therefore, the number of cycles in the interval from 0 to 2π is 1.
In summary:
Number of cycles: 1
Amplitude: 2
Sine function: -2sin(2π0)
Period: 1