The number can also be expressed by taking the Taylor series of a trigonometric function.
The mathematics is easier to deal with if we can use trigonometric functions.
In a regular calculus course, students would study trigonometric functions.
With these definitions the trigonometric functions can be defined for complex numbers.
Because squares to 1, the power series expansion of generates the trigonometric functions.
And thus, the origin of the trigonometric function named sine.
One can define the trigonometric functions also by using power series:
A unique algorithm has been developed for the calculation of trigonometric functions.
The advantage is that calculating the trigonometric functions directly can be avoided.
Trigonometric functions were among the earliest uses for mathematical tables.