Trigonometry — Math.js Reference

acos

Compute the inverse cosine of a value in radians.

Syntax

acos(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex	Function input

Returns

number | BigNumber | Complex — The arc cosine of x

Examples

acos(0.5)
acos(cos(2.3))

See Also

cos atan asin

acosh

Calculate the hyperbolic arccos of a value, defined as `acosh(x) = ln(sqrt(x^2 - 1) + x)`.

Syntax

acosh(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex	Function input

Returns

number | BigNumber | Complex — Hyperbolic arccosine of x

Examples

acosh(1.5)

See Also

cosh asinh atanh

acot

Calculate the inverse cotangent of a value.

Syntax

acot(x)

Parameters

Name	Type	Description
x	number \| BigNumber\| Complex	Function input

Returns

number | BigNumber| Complex — The arc cotangent of x

Examples

acot(0.5)
acot(cot(0.5))
acot(2)

See Also

cot atan

acoth

Calculate the inverse hyperbolic tangent of a value, defined as `acoth(x) = (ln((x+1)/x) + ln(x/(x-1))) / 2`.

Syntax

acoth(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex	Function input

Returns

number | BigNumber | Complex — Hyperbolic arccotangent of x

Examples

acoth(2)
acoth(0.5)

See Also

acsch asech

acsc

Calculate the inverse cotangent of a value.

Syntax

acsc(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex	Function input

Returns

number | BigNumber | Complex — The arc cosecant of x

Examples

acsc(2)
acsc(csc(0.5))
acsc(0.5)

See Also

csc asin asec

acsch

Calculate the inverse hyperbolic cosecant of a value, defined as `acsch(x) = ln(1/x + sqrt(1/x^2 + 1))`.

Syntax

acsch(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex	Function input

Returns

number | BigNumber | Complex — Hyperbolic arccosecant of x

Examples

acsch(0.5)

See Also

asech acoth

asec

Calculate the inverse secant of a value.

Syntax

asec(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex	Function input

Returns

number | BigNumber | Complex — The arc secant of x

Examples

asec(0.5)
asec(sec(0.5))
asec(2)

See Also

acos acot acsc

asech

Calculate the inverse secant of a value.

Syntax

asech(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex	Function input

Returns

number | BigNumber | Complex — Hyperbolic arcsecant of x

Examples

asech(0.5)

See Also

acsch acoth

asin

Compute the inverse sine of a value in radians.

Syntax

asin(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex	Function input

Returns

number | BigNumber | Complex — The arc sine of x

Examples

asin(0.5)
asin(sin(0.5))

See Also

sin acos atan

asinh

Calculate the hyperbolic arcsine of a value, defined as `asinh(x) = ln(x + sqrt(x^2 + 1))`.

Syntax

asinh(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex	Function input

Returns

number | BigNumber | Complex — Hyperbolic arcsine of x

Examples

asinh(0.5)

See Also

acosh atanh

atan

Compute the inverse tangent of a value in radians.

Syntax

atan(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex	Function input

Returns

number | BigNumber | Complex — The arc tangent of x

Examples

atan(0.5)
atan(tan(0.5))

See Also

tan acos asin

atan2

Computes the principal value of the arc tangent of y/x in radians.

Syntax

atan2(y | x)

Parameters

Name	Type	Description
y	number \| Array \| Matrix	Second dimension
x	number \| Array \| Matrix	First dimension

Returns

number | Array | Matrix — Four-quadrant inverse tangent

Examples

atan2(2
2) / pi
angle = 60 deg in rad
x = cos(angle)
y = sin(angle)

See Also

sin cos tan

atanh

Calculate the hyperbolic arctangent of a value, defined as `atanh(x) = ln((1 + x)/(1 - x)) / 2`.

Syntax

atanh(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex	Function input

Returns

number | BigNumber | Complex — Hyperbolic arctangent of x

Examples

atanh(0.5)

See Also

acosh asinh

cos

Compute the cosine of x in radians.

Syntax

cos(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex \| Unit	Function input

Returns

number | BigNumber | Complex — Cosine of x

Examples

cos(2)
cos(pi / 4) ^ 2
cos(180 deg)
cos(60 deg)
sin(0.2)^2 + cos(0.2)^2

See Also

acos sin tan

cosh

Compute the hyperbolic cosine of x in radians.

Syntax

cosh(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex	Function input

Returns

number | BigNumber | Complex — Hyperbolic cosine of x

Examples

cosh(0.5)

See Also

sinh tanh coth

cot

Compute the cotangent of x in radians. Defined as 1/tan(x)

Syntax

cot(x)

Parameters

Name	Type	Description
x	number \| Complex \| Unit \| Array \| Matrix	Function input

Returns

number | Complex | Array | Matrix — Cotangent of x

Examples

cot(2)
1 / tan(2)

See Also

sec csc tan

coth

Compute the hyperbolic cotangent of x in radians.

Syntax

coth(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex	Function input

Returns

number | BigNumber | Complex — Hyperbolic cotangent of x

Examples

coth(2)
1 / tanh(2)

See Also

sech csch tanh

csc

Compute the cosecant of x in radians. Defined as 1/sin(x)

Syntax

csc(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex \| Unit	Function input

Returns

number | BigNumber | Complex — Cosecant of x

Examples

csc(2)
1 / sin(2)

See Also

sec cot sin

csch

Compute the hyperbolic cosecant of x in radians. Defined as 1/sinh(x)

Syntax

csch(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex	Function input

Returns

number | BigNumber | Complex — Hyperbolic cosecant of x

Examples

csch(2)
1 / sinh(2)

See Also

sech coth sinh

sec

Compute the secant of x in radians. Defined as 1/cos(x)

Syntax

sec(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex \| Unit	Function input

Returns

number | BigNumber | Complex — Secant of x

Examples

sec(2)
1 / cos(2)

See Also

cot csc cos

sech

Compute the hyperbolic secant of x in radians. Defined as 1/cosh(x)

Syntax

sech(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex	Function input

Returns

number | BigNumber | Complex — Hyperbolic secant of x

Examples

sech(2)
1 / cosh(2)

See Also

coth csch cosh

sin

Compute the sine of x in radians.

Syntax

sin(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex \| Unit	Function input

Returns

number | BigNumber | Complex — Sine of x

Examples

sin(2)
sin(pi / 4) ^ 2
sin(90 deg)
sin(30 deg)
sin(0.2)^2 + cos(0.2)^2

See Also

asin cos tan

sinh

Compute the hyperbolic sine of x in radians.

Syntax

sinh(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex	Function input

Returns

number | BigNumber | Complex — Hyperbolic sine of x

Examples

sinh(0.5)

See Also

cosh tanh

tan

Compute the tangent of x in radians.

Syntax

tan(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex \| Unit	Function input

Returns

number | BigNumber | Complex — Tangent of x

Examples

tan(0.5)
sin(0.5) / cos(0.5)
tan(pi / 4)
tan(45 deg)

See Also

atan sin cos

tanh

Compute the hyperbolic tangent of x in radians.

Syntax

tanh(x)

Parameters

Name	Type	Description
x	number \| BigNumber \| Complex	Function input

Returns

number | BigNumber | Complex — Hyperbolic tangent of x

Examples

tanh(0.5)
sinh(0.5) / cosh(0.5)

See Also

sinh cosh