The sine function is classified as an odd function. This can be understood by examining the symmetry properties of the sine function with respect to the origin.
For any function to be considered odd, it must satisfy the property f(-x) = -f(x) for all x in its domain. Let’s look at the sine function:
We know that:
sin(-x) = -sin(x)
This identity shows that if we take the sine of a negative angle, it gives us the negative of the sine of the positive angle. This behavior reflects the oddness of the function on the coordinate system where the sine graph is symmetrical about the origin.
To illustrate, when you evaluate the sine function at positive and negative angles, you’ll see:
- sin(30°) = 0.5
- sin(-30°) = -0.5
Because the output for the negative input is the negative of the output for the positive input, this confirms that the sine function is indeed an odd function.