octave: Trigonometry
17.3 Trigonometry
=================
Octave provides the following trigonometric functions where angles are
specified in radians. To convert from degrees to radians multiply by
‘pi/180’ or use the ‘deg2rad’ function. For example, ‘sin (30 *
pi/180)’ returns the sine of 30 degrees. As an alternative, Octave
provides a number of trigonometric functions which work directly on an
argument specified in degrees. These functions are named after the base
trigonometric function with a ‘d’ suffix. As an example, ‘sin’ expects
an angle in radians while ‘sind’ expects an angle in degrees.
Octave uses the C library trigonometric functions. It is expected
that these functions are defined by the ISO/IEC 9899 Standard. This
Standard is available at:
<http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1124.pdf>. Section
F.9.1 deals with the trigonometric functions. The behavior of most of
the functions is relatively straightforward. However, there are some
exceptions to the standard behavior. Many of the exceptions involve the
behavior for -0. The most complex case is atan2. Octave exactly
implements the behavior given in the Standard. Including ‘atan2(+- 0,
0)’ returns ‘+- pi’.
It should be noted that MATLAB uses different definitions which
apparently do not distinguish -0.
-- : RAD = deg2rad (DEG)
Convert degrees to radians.
The input DEG must be a scalar, vector, or N-dimensional array of
double or single floating point values. DEG may be complex in
which case the real and imaginary components are converted
separately.
The output RAD is the same size and shape as DEG with degrees
converted to radians using the conversion constant ‘pi/180’.
Example:
deg2rad ([0, 90, 180, 270, 360])
⇒ 0.00000 1.57080 3.14159 4.71239 6.28319
See also: 
rad2deg XREFrad2deg.
-- : DEG = rad2deg (RAD)
Convert radians to degrees.
The input RAD must be a scalar, vector, or N-dimensional array of
double or single floating point values. RAD may be complex in
which case the real and imaginary components are converted
separately.
The output DEG is the same size and shape as RAD with radians
converted to degrees using the conversion constant ‘180/pi’.
Example:
rad2deg ([0, pi/2, pi, 3/2*pi, 2*pi])
⇒ 0 90 180 270 360
See also: deg2rad XREFdeg2rad.
-- : sin (X)
Compute the sine for each element of X in radians.
DONTPRINTYET See also: asin XREFasin, sind XREFsind, *notesinh:
DONTPRINTYET See also: asin XREFasin, sind XREFsind, sinh
XREFsinh.
-- : cos (X)
Compute the cosine for each element of X in radians.
DONTPRINTYET See also: acos XREFacos, cosd XREFcosd, *notecosh:
DONTPRINTYET See also: acos XREFacos, cosd XREFcosd, cosh
XREFcosh.
-- : tan (Z)
Compute the tangent for each element of X in radians.
DONTPRINTYET See also: atan XREFatan, tand XREFtand, *notetanh:
DONTPRINTYET See also: atan XREFatan, tand XREFtand, tanh
XREFtanh.
-- : sec (X)
Compute the secant for each element of X in radians.
DONTPRINTYET See also: asec XREFasec, secd XREFsecd, *notesech:
DONTPRINTYET See also: asec XREFasec, secd XREFsecd, sech
XREFsech.
-- : csc (X)
Compute the cosecant for each element of X in radians.
DONTPRINTYET See also: acsc XREFacsc, cscd XREFcscd, *notecsch:
DONTPRINTYET See also: acsc XREFacsc, cscd XREFcscd, csch
XREFcsch.
-- : cot (X)
Compute the cotangent for each element of X in radians.
DONTPRINTYET See also: acot XREFacot, cotd XREFcotd, *notecoth:
DONTPRINTYET See also: acot XREFacot, cotd XREFcotd, coth
XREFcoth.
-- : asin (X)
Compute the inverse sine in radians for each element of X.
See also: sin XREFsin, asind XREFasind.
-- : acos (X)
Compute the inverse cosine in radians for each element of X.
See also: cos XREFcos, acosd XREFacosd.
-- : atan (X)
Compute the inverse tangent in radians for each element of X.
See also: tan XREFtan, atand XREFatand.
-- : asec (X)
Compute the inverse secant in radians for each element of X.
See also: sec XREFsec, asecd XREFasecd.
-- : acsc (X)
Compute the inverse cosecant in radians for each element of X.
See also: csc XREFcsc, acscd XREFacscd.
-- : acot (X)
Compute the inverse cotangent in radians for each element of X.
See also: cot XREFcot, acotd XREFacotd.
-- : sinh (X)
Compute the hyperbolic sine for each element of X.
DONTPRINTYET See also: asinh XREFasinh, cosh XREFcosh, *notetanh:
DONTPRINTYET See also: asinh XREFasinh, cosh XREFcosh, tanh
XREFtanh.
-- : cosh (X)
Compute the hyperbolic cosine for each element of X.
DONTPRINTYET See also: acosh XREFacosh, sinh XREFsinh, *notetanh:
DONTPRINTYET See also: acosh XREFacosh, sinh XREFsinh, tanh
XREFtanh.
-- : tanh (X)
Compute hyperbolic tangent for each element of X.
DONTPRINTYET See also: atanh XREFatanh, sinh XREFsinh, *notecosh:
DONTPRINTYET See also: atanh XREFatanh, sinh XREFsinh, cosh
XREFcosh.
-- : sech (X)
Compute the hyperbolic secant of each element of X.
See also: asech XREFasech.
-- : csch (X)
Compute the hyperbolic cosecant of each element of X.
See also: acsch XREFacsch.
-- : coth (X)
Compute the hyperbolic cotangent of each element of X.
See also: acoth XREFacoth.
-- : asinh (X)
Compute the inverse hyperbolic sine for each element of X.
See also: sinh XREFsinh.
-- : acosh (X)
Compute the inverse hyperbolic cosine for each element of X.
See also: cosh XREFcosh.
-- : atanh (X)
Compute the inverse hyperbolic tangent for each element of X.
See also: tanh XREFtanh.
-- : asech (X)
Compute the inverse hyperbolic secant of each element of X.
See also: sech XREFsech.
-- : acsch (X)
Compute the inverse hyperbolic cosecant of each element of X.
See also: csch XREFcsch.
-- : acoth (X)
Compute the inverse hyperbolic cotangent of each element of X.
See also: coth XREFcoth.
-- : atan2 (Y, X)
Compute atan (Y / X) for corresponding elements of Y and X.
Y and X must match in size and orientation. The signs of elements
of Y and X are used to determine the quadrants of each resulting
value.
This function is equivalent to ‘arg (complex (X, Y))’.
DONTPRINTYET See also: tan XREFtan, tand XREFtand, *notetanh:
DONTPRINTYET See also: tan XREFtan, tand XREFtand, tanh
XREFtanh, atanh XREFatanh.
Octave provides the following trigonometric functions where angles
are specified in degrees. These functions produce true zeros at the
appropriate intervals rather than the small round-off error that occurs
when using radians. For example:
cosd (90)
⇒ 0
cos (pi/2)
⇒ 6.1230e-17
-- : sind (X)
Compute the sine for each element of X in degrees.
Returns zero for elements where ‘X/180’ is an integer.
See also: asind XREFasind, sin XREFsin.
-- : cosd (X)
Compute the cosine for each element of X in degrees.
Returns zero for elements where ‘(X-90)/180’ is an integer.
See also: acosd XREFacosd, cos XREFcos.
-- : tand (X)
Compute the tangent for each element of X in degrees.
Returns zero for elements where ‘X/180’ is an integer and ‘Inf’ for
elements where ‘(X-90)/180’ is an integer.
See also: atand XREFatand, tan XREFtan.
-- : secd (X)
Compute the secant for each element of X in degrees.
See also: asecd XREFasecd, sec XREFsec.
-- : cscd (X)
Compute the cosecant for each element of X in degrees.
See also: acscd XREFacscd, csc XREFcsc.
-- : cotd (X)
Compute the cotangent for each element of X in degrees.
See also: acotd XREFacotd, cot XREFcot.
-- : asind (X)
Compute the inverse sine in degrees for each element of X.
See also: sind XREFsind, asin XREFasin.
-- : acosd (X)
Compute the inverse cosine in degrees for each element of X.
See also: cosd XREFcosd, acos XREFacos.
-- : atand (X)
Compute the inverse tangent in degrees for each element of X.
See also: tand XREFtand, atan XREFatan.
-- : atan2d (Y, X)
Compute atan (Y / X) in degrees for corresponding elements from Y
and X.
See also: tand XREFtand, atan2 XREFatan2.
-- : asecd (X)
Compute the inverse secant in degrees for each element of X.
See also: secd XREFsecd, asec XREFasec.
-- : acscd (X)
Compute the inverse cosecant in degrees for each element of X.
See also: cscd XREFcscd, acsc XREFacsc.
-- : acotd (X)
Compute the inverse cotangent in degrees for each element of X.
See also: cotd XREFcotd, acot XREFacot.
Info Catalog
octave: Complex Arithmetic
octave: Arithmetic
octave: Sums and Products