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.
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.
y = atan (x) ¶Compute the inverse tangent in radians for each element of x.
y = acsc (x) ¶Compute the inverse cosecant in radians for each element of x.
y = acot (x) ¶Compute the inverse cotangent in radians for each element of x.
angle = 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)).
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
y = sind (x) ¶Compute the sine for each element of x in degrees.
The function is more accurate than sin for large values of x
and for multiples of 180 degrees (x/180 is an integer) where
sind returns 0 rather than a small value on the order of eps.
y = cosd (x) ¶Compute the cosine for each element of x in degrees.
The function is more accurate than cos for large values of x
and for multiples of 90 degrees (x = 90 + 180*n with n an
integer) where cosd returns 0 rather than a small value on the order
of eps.
y = 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.
y = acosd (x) ¶Compute the inverse cosine in degrees for each element of x.
y = atand (x) ¶Compute the inverse tangent in degrees for each element of x.
d = atan2d (y, x) ¶Compute atan (y / x) in degrees for corresponding elements from y and x.
y = asecd (x) ¶Compute the inverse secant in degrees for each element of x.
y = acscd (x) ¶Compute the inverse cosecant in degrees for each element of x.
y = acotd (x) ¶Compute the inverse cotangent in degrees for each element of x.
Finally, there are two trigonometric functions that calculate special arguments with increased accuracy.
y = sinpi (x) ¶Compute sine (x * pi) for each element of x accurately.
The ordinary sin function uses IEEE floating point numbers and may
produce results that are very close (within a few eps) of the correct
value, but which are not exact. The sinpi function is more accurate
and returns 0 exactly for integer values of x and +1/-1 for
half-integer values (e.g., …, -3/2, -1/2, 1/2, 3/2, …).
Example
comparison of sin and sinpi for integer values of x
sin ([0, 1, 2, 3] * pi)
⇒
0 1.2246e-16 -2.4493e-16 3.6739e-16
sinpi ([0, 1, 2, 3])
⇒
0 0 0 0
y = cospi (x) ¶Compute cosine (x * pi) for each element of x accurately.
The ordinary cos function uses IEEE floating point numbers and may
produce results that are very close (within a few eps) of the correct
value, but which are not exact. The cospi function is more accurate
and returns 0 exactly for half-integer values of x (e.g., …,
-3/2, -1/2, 1/2, 3/2, …), and +1/-1 for integer values.
Example
comparison of cos and cospi for half-integer values of x
cos ([-3/2, -1/2, 1/2, 3/2] * pi)
⇒
-1.8370e-16 6.1232e-17 6.1232e-17 -1.8370e-16
cospi ([-3/2, -1/2, 1/2, 3/2])
⇒
0 0 0 0