Scheme Programming/Further Maths

Trigonometric Functions
Scheme always uses radians for its internal representation of angles, so its sine, cosine, tangent, arcsine, arccosine, and arctangent functions operate as such:

Hyperbolic Functions
Scheme provides a number of hyperbolic functions, such as hyperbolic sine, cosine, tangent and their inverses.

Raising a base to a power
Scheme provides the  function to raise a base to an exponent.

Finding the square root of a number
Scheme provides a  function for finding the square root of a number.

Exponential
Scheme provides a  function for raising base $$e$$ to a power:

Logarithm
Scheme provides a  function for finding the natural logarithm of a number:

Note that there is no built-in procedure for finding any other base logarithm other than base $$e$$. Instead, you can type

Rounding functions
Scheme provides a set of functions for rounding a real number up, down or to the nearest integer:


 * - This returns the largest integer that is no larger than x.
 * - This returns the smallest integer that is no smaller than x.
 * - This returns the integer value closest to x that is no larger than the absolute value of x.
 * - This rounds value of x to the nearest integer as is usual in mathematics. It even works when halfway between values.
 * - This returns the absolute value of x.

Number theoretic division
In order to perform mathematically exact divisions and accomplish tasks for number theorists, Scheme provides a small number of division specific functions:


 * - Calculates the remainder of dividing y into x (that is, the remainder of ):


 * - Calculates the modulo of x and y.

There is clearly a difference between modulo and remainder, one of them not shown here is that remainder is the only one which will return an inexact value, and can take inexact arguments.