The shift-S
(calc-sin) [sin] command computes the
sine of an angle or complex number. If the input is an HMS form,
it is interpreted as degrees-minutes-seconds; otherwise, the
input is interpreted according to the current angular mode. It is
best to use Radians mode when operating on complex numbers.
Calc's “units” mechanism includes angular units
like deg, rad, and grad.
While ‘sin(45
deg)’ is not evaluated all the time, the
u s (calc-simplify-units) command will
simplify ‘sin(45
deg)’ by taking the sine of 45 degrees,
regardless of the current angular mode. See Basic
Operations on Units.
Also, the symbolic variable pi is not ordinarily
recognized in arguments to trigonometric functions, as in
‘sin(3 pi /
4)’, but the a s
(calc-simplify) command recognizes many such
formulas when the current angular mode is Radians and
Symbolic mode is enabled; this example would be replaced by
‘sqrt(2) / 2’.
See Symbolic Mode.
Beware, this simplification occurs even if you have stored a
different value in the variable ‘pi’; this is one reason why changing
built-in variables is a bad idea. Arguments of the form
‘x’ plus a
multiple of ‘pi/2’ are also simplified. Calc
includes similar formulas for cos and
tan.
The a s command knows all angles which are integer multiples of ‘pi/12’, ‘pi/10’, or ‘pi/8’ radians. In Degrees mode, analogous simplifications occur for integer multiples of 15 or 18 degrees, and for arguments plus multiples of 90 degrees.
With the Inverse flag,
calc-sin computes an arcsine. This is also available
as the calc-arcsin command or arcsin
algebraic function. The returned argument is converted to
degrees, radians, or HMS notation depending on the current
angular mode.
With the Hyperbolic flag,
calc-sin computes the hyperbolic sine, also
available as calc-sinh [sinh]. With the
Hyperbolic and Inverse flags, it computes the hyperbolic arcsine
(calc-arcsinh) [arcsinh].
The shift-C
(calc-cos) [cos] command computes the
cosine of an angle or complex number, and shift-T
(calc-tan) [tan] computes the tangent,
along with all the various inverse and hyperbolic variants of
these functions.
The f T
(calc-arctan2) [arctan2] command takes
two numbers from the stack and computes the arc tangent of their
ratio. The result is in the full range from -180
(exclusive) to +180 (inclusive) degrees, or the analogous
range in radians. A similar result would be obtained with
/ followed by I T, but the value would only
be in the range from -90 to +90 degrees since the
division loses information about the signs of the two components,
and an error might result from an explicit division by zero which
arctan2 would avoid. By (arbitrary) definition,
‘arctan2(0,0)=0’.
The calc-sincos
[sincos] command computes the sine and cosine of a
number, returning them as a vector of the form
‘[cos,
sin]’. With the
Inverse flag [arcsincos], this command takes a
two-element vector as an argument and computes
arctan2 of the elements. (This command does not
accept the Hyperbolic flag.)
The remaining trigonometric functions,
calc-sec [sec], calc-csc
[csc] and calc-cot [cot],
are also available. With the Hyperbolic flag, these compute their
hyperbolic counterparts, which are also available separately as
calc-sech [sech],
calc-csch [csch] and
calc-coth [coth]. (These commands do
not accept the Inverse flag.)