Trigonometric/Hyperbolic Functions
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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.  *Note
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.)