Re: SINC function (WP 34S) Message #14 Posted by Manolo Sobrino on 24 Aug 2013, 12:48 a.m., in response to message #6 by Paul Dale
Ahem... this... misconception... again.
Let's get this over with. Degrees are practical units of angular measurement. They only make sense as arguments of circular functions (with real domain). You could measure everything in degrees provided you scaled every other variable accordingly.
x > x *Pi/180
In fact, you are scaling the variable too in the trigonometric function, it's just you're being quiet about it:
Let's consider the Taylor series for SIN(x). Everyone here will agree with:
SIN(x)= x  x^3/3! + x^5/5! + ...
You can use this to calculate, say SIN(30º):
SIN(x=30º)= 30º  30º^3/3! + 30º^5/5! + ... = 0.5
Please, evaluate this expression taking 30º as just x=30 and see what happens. What's going on?
The series works for x in radians, and for x in degrees we can drop the degree (º) as long as we write it down as:
SIN(x)= x*Pi/180  (x*Pi/180)^3/3! + (x*Pi/180)^5/5! + ...
Please evaluate:
SIN(30º)= 30*Pi/180  (30*Pi/180)^3/3! + (30*Pi/180)^5/5! + ...
Now you got it right!
You can "define" SINC in degrees as long as it is:
SINC(xº) = (180/Pi)* SIN(xº)/x
But you really don't want to use degrees for anything but real trigonometric functions... and then just to write the angles down.
