Its hyperbolic form can be written as the sum of e to the x plus e to the negative x all divided by two, and the first three terms of its Taylor series expansion are 1, minus x squared over two, plus x to the fourth over 24.
In a certain range it can be approximated using Hardy's approximation and it has a fixed point at Dottie's number, a value roughly equal to .74. A discrete transform of this type is used in compressing JPEG images and its hyperbolic form can be used to describe the shape of a catenary. The dot product between two vectors is equal to their norms times this function. Its hyperbolic form can be written as the sum of e to the x plus e to the negative x all divided by two, and the first three terms of its Taylor series expansion are 1, minus x squared over two, plus x to the fourth over 24. FTP, name this function that is the multiplicative inverse of the secant function and can be calculated in a right triangle as adjacent divided by hypotenuse. 
In a certain range it can be approximated using Hardy's approximation and it has a fixed point at Dottie's number, a value roughly equal to .74.
{Cosine} function