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 = -6sinπ0
show your work/steps
The given sine function is y = -6sin(π0).
To find the number of cycles in the interval from 0 to 2π, we need to look at the period of the sine function. The period of a sine function can be found using the formula:
Period = 2π / coefficient of x
In this case, the coefficient of x is π, so the period is:
Period = 2π / π = 2
Therefore, the sine function completes 2 cycles in the interval from 0 to 2π.
Next, let's find the amplitude of the function. The general equation of a sine function is y = A*sin(Bx + C) + D, where A is the amplitude. In this case, the equation is y = -6sin(π0), which can be written as y = -6sin(0).
Since sin(0) = 0, the equation simplifies to y = -6 * 0, which is y = 0. Hence, the amplitude of the function is 0.
To summarize:
- The number of cycles in the interval from 0 to 2π is 2.
- The amplitude of the function is 0.
- The period of the function is 2.