Expert: Paul Klarreich - 10/21/2005

Question
hi there . . . i am a second year ap calc teacher and the other day my class and i were solving a related rates problem about changing angles, and it turned out that the answer was exactly the same in either radians or degrees.  what is up with that . . . and also what are the units used when calculating the sine or cosine of an angle?

Answer
Hi, Matthew,
I wasn't aware there was such a thing as second year AP calculus.  

OH -- you mean it's YOUR second year.

Enough of that stuff.

I am not sure exactly what the example said, so it would seem a bit strange that the answer comes out the same both ways, but perhaps the units were irrelevant.  Why don't you send the actual problem?

Ordinarily, when we write  y = sin x, we mean 'x' is assumed to be in radian measure, and certainly when we get to things like power series, it has to be.  If we write:

sin x = x - x^3/3! + x^5/5! - ...

then 'x' is definitely in radians.  

Send the problem along.  I am curious to see what happened.

Paul