What is the usual period for sine?

Answer 1

Periodic functions are those functions for which the value of the dependent variable repeats itself for certain values of the dependent variable.

example:

F(x)=y

x is the dependent variable (output of the function)

y is the independent variable (input of the function)

F(x1)=y1

F(x2)=y1

As you can see the value of the function is the same for two different values of the dependent variable.

The smallest difference between any two dependent variables giving the same value of the function is the period of the function.

The periodicity of the usual sine function is 2pi. This is how it works:

F(X)=sin(X)

sin(x1)=y

sin(x2)=sin(x1+2pi)=y

sin(x3)=sin(x1+4pi)=y

The smallest difference between any two independent variables (x1 or x2 or x3) is 2pi.

This is also evident from the general sine curve (graphical representation). The sine function has a fixed range from -1 to 1 (i.e.,for sin(x)=y, y can only lie between -1 and 1). So, the interval (difference in values of the independent variable) after which the nature of the wave repeats is it's period. Look at the graph and you'll see that the wave replicates after covering 2pi from the current point.