(octave.info)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: Note: rad2deg.
-- : 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: Note: deg2rad.
-- : sin (X)
Compute the sine for each element of X in radians.
See also: Note: asin, Note: sind, *note sinh:
XREFsinh.
-- : cos (X)
Compute the cosine for each element of X in radians.
See also: Note: acos, Note: cosd, *note cosh:
XREFcosh.
-- : tan (Z)
Compute the tangent for each element of X in radians.
See also: Note: atan, Note: tand, *note tanh:
XREFtanh.
-- : sec (X)
Compute the secant for each element of X in radians.
See also: Note: asec, Note: secd, *note sech:
XREFsech.
-- : csc (X)
Compute the cosecant for each element of X in radians.
See also: Note: acsc, Note: cscd, *note csch:
XREFcsch.
-- : cot (X)
Compute the cotangent for each element of X in radians.
See also: Note: acot, Note: cotd, *note coth:
XREFcoth.
-- : asin (X)
Compute the inverse sine in radians for each element of X.
See also: Note: sin, Note: asind.
-- : acos (X)
Compute the inverse cosine in radians for each element of X.
See also: Note: cos, Note: acosd.
-- : atan (X)
Compute the inverse tangent in radians for each element of X.
See also: Note: tan, Note: atand.
-- : asec (X)
Compute the inverse secant in radians for each element of X.
See also: Note: sec, Note: asecd.
-- : acsc (X)
Compute the inverse cosecant in radians for each element of X.
See also: Note: csc, Note: acscd.
-- : acot (X)
Compute the inverse cotangent in radians for each element of X.
See also: Note: cot, Note: acotd.
-- : sinh (X)
Compute the hyperbolic sine for each element of X.
See also: Note: asinh, Note: cosh, *note tanh:
XREFtanh.
-- : cosh (X)
Compute the hyperbolic cosine for each element of X.
See also: Note: acosh, Note: sinh, *note tanh:
XREFtanh.
-- : tanh (X)
Compute hyperbolic tangent for each element of X.
See also: Note: atanh, Note: sinh, *note cosh:
XREFcosh.
-- : sech (X)
Compute the hyperbolic secant of each element of X.
See also: Note: asech.
-- : csch (X)
Compute the hyperbolic cosecant of each element of X.
See also: Note: acsch.
-- : coth (X)
Compute the hyperbolic cotangent of each element of X.
See also: Note: acoth.
-- : asinh (X)
Compute the inverse hyperbolic sine for each element of X.
See also: Note: sinh.
-- : acosh (X)
Compute the inverse hyperbolic cosine for each element of X.
See also: Note: cosh.
-- : atanh (X)
Compute the inverse hyperbolic tangent for each element of X.
See also: Note: tanh.
-- : asech (X)
Compute the inverse hyperbolic secant of each element of X.
See also: Note: sech.
-- : acsch (X)
Compute the inverse hyperbolic cosecant of each element of X.
See also: Note: csch.
-- : acoth (X)
Compute the inverse hyperbolic cotangent of each element of X.
See also: Note: coth.
-- : 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))’.
See also: Note: tan, Note: tand, *note tanh:
XREFtanh, Note: atanh.
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: Note: asind, Note: sin.
-- : 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: Note: acosd, Note: cos.
-- : 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: Note: atand, Note: tan.
-- : secd (X)
Compute the secant for each element of X in degrees.
See also: Note: asecd, Note: sec.
-- : cscd (X)
Compute the cosecant for each element of X in degrees.
See also: Note: acscd, Note: csc.
-- : cotd (X)
Compute the cotangent for each element of X in degrees.
See also: Note: acotd, Note: cot.
-- : asind (X)
Compute the inverse sine in degrees for each element of X.
See also: Note: sind, Note: asin.
-- : acosd (X)
Compute the inverse cosine in degrees for each element of X.
See also: Note: cosd, Note: acos.
-- : atand (X)
Compute the inverse tangent in degrees for each element of X.
See also: Note: tand, Note: atan.
-- : atan2d (Y, X)
Compute atan (Y / X) in degrees for corresponding elements from Y
and X.
See also: Note: tand, Note: atan2.
-- : asecd (X)
Compute the inverse secant in degrees for each element of X.
See also: Note: secd, Note: asec.
-- : acscd (X)
Compute the inverse cosecant in degrees for each element of X.
See also: Note: cscd, Note: acsc.
-- : acotd (X)
Compute the inverse cotangent in degrees for each element of X.
See also: Note: cotd, Note: acot.
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