Sin(x)/x as x approaches 0 returns 1 when x
is used as the argument to sin and as the denominator in the fraction,
or if the same function f(x) = 0 is used as both
argument and denominator. In the case where g(x) = sin(x)
and f(x) = x, g(x)/f(x)
returns 0, following the normal Mathcad rules
for the fraction 0/0. If you wish to guarantee you
get the correct behavior, use sinc.
Trig functions are subject to roundoff errors in the following cases:
For large arguments, >1012 in
magnitude, trig functions begin to lose precision. When this happens,
you see the error message "Cannot evaluate this accurately at
one or more of the points specified."
The tan function has singularities, and is undefined at odd-integer
multiples of π/2. Arguments near these singularities
are subject to precision errors.
The value of π on a computer is only an
approximation, so arguments to the trig functions near multiples of π
can only be an approximation of the correct value. If you need more exact
values, use symbolic evaluation
with a decimal point, to force floating point calculations.
Many of these comments also apply to the hyperbolic trig functions.