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 = -6 sin π0
The given sine function is y = -6 sin(π0).
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 cycle in that interval. In this case, the function is y = -6 sin(π0), which simplifies to y = -6 sin(0).
Since sin(0) = 0, the function is y = -6(0) = 0 for all values of x in the interval from 0 to 2π. In other words, the function does not complete any cycles in this interval.
The amplitude of the function can be found by looking at the coefficient in front of the sine function. In this case, the amplitude is the absolute value of -6, which is 6.
The period of a sine function is the length of one full cycle. Since the given function y = -6 sin(π0) does not complete any cycles, it does not have a defined period.