edp@jareth.enet.dec.com (Always mount a scratch monkey.) (10/11/90)
I apologize for harping on this, but I've been trying to think of a better answer than I gave before to explain why the derivative of sine-in-degrees is different than the derivative of sine-in-radians. I think these questions illuminate the difference: How much does sin(x) change when x changes by one radian? How much does sin(x) change when x changes by one degree? Obviously, the sine changes much more when x is changed by a radian than when it is changed by a degree. And that's why the derivatives are different. Note that derivative is defined upon a function whose domain and range are both numbers. Although we can define sines of angles, we cannot take the derivative of functions defined as sines of angles. We have to define a function which takes a NUMBER and produces a NUMBER, then we can take the derivative of that function. One possibility is to define sin(x) as the sine of x degrees. Another possibility is to define sin(x) as the sine of x radians. But these are different functions; they have different derivatives. -- edp (Eric Postpischil) "Always mount a scratch monkey." edp@jareth.enet.dec.com