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### 17.3 Trigonometry

Octave provides the following trigonometric functions. Angles are specified in radians. To convert from degrees to radians multiply by `pi/180` (e.g. `sin (30 * pi/180)` returns the sine of 30 degrees).

— Mapping Function: sin (x)

> Compute the sine of each element of x.

— Mapping Function: cos (x)

> Compute the cosine of each element of x.

— Mapping Function: tan (z)

> Compute tangent of each element of x.

— Mapping Function: sec (x)

> Compute the secant of each element of x.

— Mapping Function: csc (x)

> Compute the cosecant of each element of x.

— Mapping Function: cot (x)

> Compute the cotangent of each element of x.

— Mapping Function: asin (x)

> Compute the inverse sine of each element of x.

— Mapping Function: acos (x)

> Compute the inverse cosine of each element of x.

— Mapping Function: atan (x)

> Compute the inverse tangent of each element of x.

— Mapping Function: asec (x)

> Compute the inverse secant of each element of x.

— Mapping Function: acsc (x)

> Compute the inverse cosecant of each element of x.

— Mapping Function: acot (x)

> Compute the inverse cotangent of each element of x.

— Mapping Function: sinh (x)

> Compute the hyperbolic sine of each element of x.

— Mapping Function: cosh (x)

> Compute the hyperbolic cosine of each element of x.

— Mapping Function: tanh (x)

> Compute hyperbolic tangent of each element of x.

— Mapping Function: sech (x)

> Compute the hyperbolic secant of each element of x.

— Mapping Function: csch (x)

> Compute the hyperbolic cosecant of each element of x.

— Mapping Function: coth (x)

> Compute the hyperbolic cotangent of each element of x.

— Mapping Function: asinh (x)

> Compute the inverse hyperbolic sine of each element of x.

— Mapping Function: acosh (x)

> Compute the inverse hyperbolic cosine of each element of x.

— Mapping Function: atanh (x)

> Compute the inverse hyperbolic tangent of each element of x.

— Mapping Function: asech (x)

> Compute the inverse hyperbolic secant of each element of x.

— Mapping Function: acsch (x)

> Compute the inverse hyperbolic cosecant of each element of x.

— Mapping Function: acoth (x)

> Compute the inverse hyperbolic cotangent of each element of x.

Each of these functions expects a single argument. For matrix arguments, they work on an element by element basis. For example,

         sin ([1, 2; 3, 4])
                0.84147   0.90930
                  0.14112  -0.75680

— Mapping Function: atan2 (y, x)

> Compute atan (y / x) for corresponding elements of y and x. The result is in the range -pi to pi.

In addition to the trigonometric functions that work with radians, Octave also provides the following functions which work with degrees.

— Function File: sind (x)

> Compute the sine of each element of x. Returns zero in elements for which x`/180` is an integer.

> See also: sin, cosd, tand, acosd, asind, atand.

— Function File: cosd (x)

> Compute the cosine of an angle in degrees. Returns zero in elements for which `(`x`-90)/180` is an integer.

> See also: cos, sind, tand, acosd, asind, atand.

— Function File: tand (x)

> Compute the tangent of an angle in degrees. Returns zero for elements of for which x`/180` is an integer and `Inf` for elements where `(`x`-90)/180` is an integer.

> See also: tan, cosd, sind, acosd, asind, atand.

— Function File: secd (x)

> Compute the secant of an angle in degrees.

> See also: sec, cscd, sind, cosd.

— Function File: cscd (x)

> Compute the cosecant of an angle in degrees.

> See also: csc, secd, sind, cosd.

— Function File: cotd (x)

> Compute the cotangent of an angle in degrees.

> See also: cot, tand.

— Function File: asind (x)

> Compute the inverse sine of an angle in degrees.

> See also: asin, sind, acosd.

— Function File: acosd (x)

> Compute the inverse cosine of an angle in degrees.

> See also: acos, cosd, asecd.

— Function File: atand (x)

> Compute the inverse tangent of an angle in degrees.

> See also: acot, tand.

— Function File: asecd (x)

> Compute inverse secant in degrees.

> See also: asec, secd, acscd.

— Function File: acscd (x)

> Compute the inverse cosecant of an angle in degrees.

> See also: acsc, cscd, asecd.

— Function File: acotd (x)

> Compute the inverse cotangent of an angle in degrees.

> See also: atan, tand.