✏️ Editing: cdesc-Math.ri Read Only

U:RDoc::NormalModule[iI"	Math:ET@0o:RDoc::Markup::Document:@parts[o;;[=o:RDoc::Markup::Paragraph;[I"=\Module \Math provides methods for basic trigonometric, ;TI"Ilogarithmic, and transcendental functions, and for extracting roots.;To:RDoc::Markup::BlankLine�o;	;[I"7You can write its constants and method calls thus:;T@o:RDoc::Markup::Verbatim;[	I"*Math::PI      # => 3.141592653589793
;TI"*Math::E       # => 2.718281828459045
;TI"Math.sin(0.0) # => 0.0
;TI"Math.cos(0.0) # => 1.0
;T:@format0o;	;[I">If you include module \Math, you can write simpler forms:;T@o;;[
I"include Math
;TI"%PI       # => 3.141592653589793
;TI"%E        # => 2.718281828459045
;TI"sin(0.0) # => 0.0
;TI"cos(0.0) # => 1.0
;T;0o;	;[I".For simplicity, the examples here assume:;T@o;;[I"include Math
;TI" INFINITY = Float::INFINITY
;T;0o;	;[I",The domains and ranges for the methods ;TI".are denoted by open or closed intervals, ;TI"9using, respectively, parentheses or square brackets:;T@o:RDoc::Markup::List:
@type:BULLET:@items[o:RDoc::Markup::ListItem:@label0;[o;	;[I"5An open interval does not include the endpoints:;T@o;;[I"(-INFINITY, INFINITY)
;T;0o;;0;[o;	;[I".A closed interval includes the endpoints:;T@o;;[I"[-1.0, 1.0]
;T;0o;;0;[o;	;[I"CA half-open interval includes one endpoint, but not the other:;T@o;;[I"[1.0, INFINITY)
;T;0o;	;[	I"IMany values returned by \Math methods are numerical approximations. ;TI";This is because many such values are, in mathematics, ;TI";of infinite precision, while in numerical computation ;TI"the precision is finite.;T@o;	;[I"=Thus, in mathematics, <i>cos(π/2)</i> is exactly zero, ;TI"Nbut in our computation <tt>cos(PI/2)</tt> is a number very close to zero:;T@o;;[I"*cos(PI/2) # => 6.123031769111886e-17
;T;0o;	;[I"4For very large and very small returned values, ;TI"1we have added formatted numbers for clarity:;T@o;;[I"Ctan(PI/2)  # => 1.633123935319537e+16   # 16331239353195370.0
;TI"Ctan(PI)    # => -1.2246467991473532e-16 # -0.0000000000000001
;T;0o;	;[I"'See class Float for the constants ;TI"2that affect Ruby's floating-point arithmetic.;T@S:RDoc::Markup::Heading:
leveli:	textI"What's Here;T@S;;i	;I"Trigonometric Functions;T@o;
;;;[o;;0;[o;	;[I"5::cos: Returns the cosine of the given argument.;To;;0;[o;	;[I"3::sin: Returns the sine of the given argument.;To;;0;[o;	;[I"6::tan: Returns the tangent of the given argument.;T@S;;i	;I"$Inverse Trigonometric Functions;T@o;
;;;[	o;;0;[o;	;[I":::acos: Returns the arc cosine of the given argument.;To;;0;[o;	;[I"8::asin: Returns the arc sine of the given argument.;To;;0;[o;	;[I";::atan: Returns the arc tangent of the given argument.;To;;0;[o;	;[I"=::atan2: Returns the arg tangent of two given arguments.;T@S;;i	;I"'Hyperbolic Trigonometric Functions;T@o;
;;;[o;;0;[o;	;[I"A::cosh: Returns the hyperbolic cosine of the given argument.;To;;0;[o;	;[I"?::sinh: Returns the hyperbolic sine of the given argument.;To;;0;[o;	;[I"B::tanh: Returns the hyperbolic tangent of the given argument.;T@S;;i	;I"/Inverse Hyperbolic Trigonometric Functions;T@o;
;;;[o;;0;[o;	;[I"J::acosh: Returns the inverse hyperbolic cosine of the given argument.;To;;0;[o;	;[I"H::asinh: Returns the inverse hyperbolic sine of the given argument.;To;;0;[o;	;[I"K::atanh: Returns the inverse hyperbolic tangent of the given argument.;T@S;;i	;I"-Exponentiation and Logarithmic Functions;T@o;
;;;[	o;;0;[o;	;[I"G::exp: Returns the value of a given value raised to a given power.;To;;0;[o;	;[I"C::log: Returns the logarithm of a given value in a given base.;To;;0;[o;	;[I"B::log10: Returns the base 10 logarithm of the given argument.;To;;0;[o;	;[I"@::log2: Returns the base 2 logarithm of the given argument.;T@S;;i	;I"$Fraction and Exponent Functions;T@o;
;;;[o;;0;[o;	;[I"F::frexp: Returns the fraction and exponent of the given argument.;To;;0;[o;	;[I"B::ldexp: Returns the value for a given fraction and exponent.;T@S;;i	;I"Root Functions;T@o;
;;;[o;;0;[o;	;[I"9::cbrt: Returns the cube root of the given argument.;To;;0;[o;	;[I";::sqrt: Returns the square root of the given argument.;T@S;;i	;I"Error Functions;T@o;
;;;[o;;0;[o;	;[I"Q::erf: Returns the value of the Gauss error function for the given argument.;To;;0;[o;	;[I"C::erfc: Returns the value of the complementary error function ;TI"for the given argument.;T@S;;i	;I"Gamma Functions;T@o;
;;;[o;;0;[o;	;[I"M::gamma: Returns the value of the gamma function for the given argument.;To;;0;[o;	;[I"C::lgamma: Returns the value of the logarithmic gamma function ;TI"for the given argument.;T@S;;i	;I"Hypotenuse Function;T@o;
;;;[o;;0;[o;	;[I"K::hypot: Returns <tt>sqrt(a**2 + b**2)</tt> for the given +a+ and +b+.;T:
@fileI"math.c;T:0@omit_headings_from_table_of_contents_below0;0;0[�[U:RDoc::Constant[i�I"PI;TI"
Math::PI;T:public0o;;[o;	;[I"BDefinition of the mathematical constant PI as a Float number.;T@;@;0@@cRDoc::NormalModule0U;[i�I"E;TI"Math::E;T;0o;;[o;	;[I"XDefinition of the mathematical constant E for Euler's number (e) as a Float number.;T@;@;0@@@0[�[[I"
class;T[[;[�[:protected[�[:private[[I"	acos;TI"math.c;T[I"
acosh;T@/[I"	asin;T@/[I"
asinh;T@/[I"	atan;T@/[I"
atan2;T@/[I"
atanh;T@/[I"	cbrt;T@/[I"cos;T@/[I"	cosh;T@/[I"erf;T@/[I"	erfc;T@/[I"exp;T@/[I"
frexp;T@/[I"
gamma;T@/[I"
hypot;T@/[I"
ldexp;T@/[I"lgamma;T@/[I"log;T@/[I"
log10;T@/[I"	log2;T@/[I"sin;T@/[I"	sinh;T@/[I"	sqrt;T@/[I"tan;T@/[I"	tanh;T@/[I"
instance;T[[;[�[;[�[;[�[�[U:RDoc::Context::Section[i�0o;;[�;0;0[I"math.c;T@cRDoc::TopLevel

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