# Taylor Series

A taylor series is a tool in mathematics to define a function in terms of an infinite power series. As long as the series **converges**, as is the case with the sine function, cosine function and exponential function, it is a very useful way to define functions.

The exponential function can be defined using a Taylor Series expanded around 0 using two of its properties.

## Links

The sine function returns the sine of a number provided in radians. In geometric terms, given the angle of a right-triangle as input, the function returns the ratio of the triangle's opposite side over its hypotenuse.

The cosine function returns the cosine of an angle provided in radians. In geometric terms, the function returns the ratio of the right-triangle's adjacent side over its hypotenuse.

The exponential function models exponential growth. The output of the function at any given point is equal to the rate of change at that point. For real number input, the function conceptually returns Euler's number raised to the value of the input.