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:
> (sin 0)
0.0
> (cos 0)
1.0
> (tan 0)
0.0
> (asin 1)
1.5707963267948965
> (acos 0)
1.5707963267948965
> (atan 1)
0.7853981633974483
Hyperbolic Functions
Scheme provides a number of hyperbolic functions, such as hyperbolic sine, cosine, tangent and their inverses.
> (sinh 0)
0.0
> (cosh 0)
1.0
> (tanh 1)
0.7615941559557649
> (asinh 0)
0.0
> (acosh 1)
0.0
> (atanh 0)
0.0
Power Functions
Raising a base to a power
Scheme provides the expt function to raise a base to an exponent.
> (expt 2 10)
1024
Finding the square root of a number
Scheme provides a sqrt function for finding the square root of a number.
> (sqrt 2)
1.4142135623730951
> (expt 2 0.5)
1.4142135623730951
Exponential and logarithmic functions
Exponential
Scheme provides a exp function for raising base to a power:
> (exp 2)
7.3890560989306504
Logarithm
Scheme provides a log function for finding the natural logarithm of a number:
> (log 7.389056)
1.999999986611192
Note that there is no built-in procedure for finding any other base logarithm other than base . Instead, you can type
> (define logB
(lambda (x B)
(/ (log x) (log B))))
Other useful maths functions (rounding, modulo, gcd, etc.)
Rounding functions
Scheme provides a set of functions for rounding a real number up, down or to the nearest integer:
(floor x)- This returns the largest integer that is no larger than x.(ceiling x)- This returns the smallest integer that is no smaller than x.(truncate x)- This returns the integer value closest to x that is no larger than the absolute value of x.(round x)- This rounds value of x to the nearest integer as is usual in mathematics. It even works when halfway between values.(abs x)- 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:
(remainder x y)- Calculates the remainder of dividing y into x (that is, the remainder ofx/y):
> (remainder 5 4)
1
> (remainder -5 4)
-1
> (remainder 5 -4)
1
> (remainder -5 -4)
-1
> (remainder x y)
error
> (remainder 2 1)
0
(modulo x y)- Calculates the modulo of x and y.
> (modulo 5 4)
1
> (modulo -5 4)
3
> (modulo 5 -4)
-3
> (modulo -5 -4)
-1
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.