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 GNU Octave Manual Version 3 by John W. Eaton, David Bateman, Søren HaubergPaperback (6"x9"), 568 pagesISBN 095461206XRRP £24.95 (\$39.95)

## 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.

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

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.

Function File: secd (x)
Compute the secant of an angle in degrees.

Function File: cscd (x)
Compute the cosecant of an angle in degrees.

Function File: cotd (x)
Compute the cotangent of an angle in degrees.

Function File: asind (x)
Compute the inverse sine of an angle in degrees.

Function File: acosd (x)
Compute the inverse cosine of an angle in degrees.

Function File: atand (x)
Compute the inverse tangent of an angle in degrees.

Function File: asecd (x)
Compute inverse secant in degrees.

Function File: acscd (x)
Compute the inverse cosecant of an angle in degrees.

Function File: acotd (x)
Compute the inverse cotangent of an angle in degrees.