In a sinusoidal,function, how do you determine whether or not y= sin4(x) has a period of 2 pi
If it is equal to 2 pi then what is a sinusoidal function that is not equal to 2 pi
To determine whether the function y = sin(4x) has a period of 2π, we can use the formula for the period of a general sinusoidal function:
Period = (2π) / |b|
In this case, the coefficient of x is 4 (b = 4). Therefore,
Period = (2π) / |4|
The absolute value of 4 is just 4, so the period of y = sin(4x) is:
Period = (2π) / 4 = π/2
Since the period is not equal to 2π, the function y = sin(4x) does not have a period of 2π.
If you are looking for a sinusoidal function that does have a period of 2π, you can consider the function y = sin(x). This is the most basic sine function, and its period is indeed 2π.