ruby--ruby/doc/math/math.rdoc

\Module \Math provides methods for basic trigonometric,
logarithmic, and transcendental functions, and for extracting roots.

You can write its constants and method calls thus:

  Math::PI      # => 3.141592653589793
  Math::E       # => 2.718281828459045
  Math.sin(0.0) # => 0.0
  Math.cos(0.0) # => 1.0

If you include module \Math, you can write simpler forms:

  include Math
  PI       # => 3.141592653589793
  E        # => 2.718281828459045
  sin(0.0) # => 0.0
  cos(0.0) # => 1.0

For simplicity, the examples here assume:

  include Math
  INFINITY = Float::INFINITY

The domains and ranges for the methods
are denoted by open or closed intervals,
using, respectively, parentheses or square brackets:

- An open interval does not include the endpoints:

    (-INFINITY, INFINITY)

- A closed interval includes the endpoints:

    [-1.0, 1.0]

- A half-open interval includes one endpoint, but not the other:

   [1.0, INFINITY)

Many values returned by \Math methods are numerical approximations.
This is because many such values are, in mathematics,
of infinite precision, while in numerical computation
the precision is finite.

Thus, in mathematics, <i>cos(π/2)</i> is exactly zero,
but in our computation <tt>cos(PI/2)</tt> is a number very close to zero:

  cos(PI/2) # => 6.123031769111886e-17

For very large and very small returned values,
we have added formatted numbers for clarity:

  tan(PI/2)  # => 1.633123935319537e+16   # 16331239353195370.0
  tan(PI)    # => -1.2246467991473532e-16 # -0.0000000000000001

See class Float for the constants
that affect Ruby's floating-point arithmetic.

=== What's Here

==== Trigonometric Functions

- ::cos: Returns the cosine of the given argument.
- ::sin: Returns the sine of the given argument.
- ::tan: Returns the tangent of the given argument.

==== Inverse Trigonometric Functions

- ::acos: Returns the arc cosine of the given argument.
- ::asin: Returns the arc sine of the given argument.
- ::atan: Returns the arc tangent of the given argument.
- ::atan2: Returns the arg tangent of two given arguments.

==== Hyperbolic Trigonometric Functions

- ::cosh: Returns the hyperbolic cosine of the given argument.
- ::sinh: Returns the hyperbolic sine of the given argument.
- ::tanh: Returns the hyperbolic tangent of the given argument.

==== Inverse Hyperbolic Trigonometric Functions

- ::acosh: Returns the inverse hyperbolic cosine of the given argument.
- ::asinh: Returns the inverse hyperbolic sine of the given argument.
- ::atanh: Returns the inverse hyperbolic tangent of the given argument.

==== Exponentiation and Logarithmic Functions

- ::exp: Returns the value of a given value raised to a given power.
- ::log: Returns the logarithm of a given value in a given base.
- ::log10: Returns the base 10 logarithm of the given argument.
- ::log2: Returns the base 2 logarithm of the given argument.

==== Fraction and Exponent Functions

- ::frexp: Returns the fraction and exponent of the given argument.
- ::ldexp: Returns the value for a given fraction and exponent.

==== Root Functions

- ::cbrt: Returns the cube root of the given argument.
- ::sqrt: Returns the square root of the given argument.

==== Error Functions

- ::erf: Returns the value of the Gauss error function for the given argument.
- ::erfc: Returns the value of the complementary error function
  for the given argument.

==== Gamma Functions

- ::gamma: Returns the value of the gamma function for the given argument.
- ::lgamma: Returns the value of the logarithmic gamma function
  for the given argument.

==== Hypotenuse Function

- ::hypot: Returns <tt>sqrt(a**2 + b**2)</tt> for the given +a+ and +b+.