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A Sinusoidal function or sine wave is a function of an oscillation. Its name is derived from sine. Sinusoidal functions are very common in science and mathematics, as many natural patterns oscillate (such as physical waves, electromagnetic radiation, etc.)

## Properties

The graph of $f(x) = \sin(x)$ has an amplitude (maximum distance from x-axis) of 1 and a frequency (length of function before it repeats) of $2\pi$. Its y-intercept is 0. The graph of $f(x) = \cos(x)$ has the same frequency and amplitude but has a y-intercept of 1.

The derivative of $f(x) = \sin(x)$ is $f(x) = \cos(x)$. The derivative of this is $f(x) = -\sin(x)$