Sinusoidal function

A sinusoidal function in blue, approximated by its Taylor polynomial.

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 period (length of function before it repeats) of $2\pi$. Its y-intercept is 0. The graph of $f(x) = \cos(x)$ has the same period and amplitude but has a phase shift of $\dfrac{\pi}{2}$, giving it a y-intercept of 1.

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