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 July 7th, 2019, 02:37 PM #1 Member     Joined: Feb 2019 From: United Kingdom Posts: 44 Thanks: 3 Why radians and not degrees in calculus? I know it's stating the obvious elephant in the room when it comes to calculus and that you should always use radian measure anytime you use trig'; I've just always accepted it as a rule. But I've never once witnessed someone give a sound geometrical argument why this is so. Could someone give a bit of geometric rigour why we use radians in calculus please.
July 7th, 2019, 04:28 PM   #2
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 Originally Posted by NineDivines I know it's stating the obvious elephant in the room when it comes to calculus and that you should always use radian measure anytime you use trig'; I've just always accepted it as a rule. But I've never once witnessed someone give a sound geometrical argument why this is so. Could someone give a bit of geometric rigour why we use radians in calculus please.
The derivative of sin(x) is cos(x) when x is in radians. (This is fairly simple to show due to the equation $\displaystyle s = r \theta$.)

The derivative of sin(x) is $\displaystyle \frac{\pi}{180} \cos(x)$ when x is in degrees.

It's just messier with the angles in degrees.

-Dan

Last edited by skipjack; July 7th, 2019 at 06:09 PM.

 July 8th, 2019, 06:40 PM #3 Senior Member   Joined: Jun 2019 From: USA Posts: 177 Thanks: 69 Was also touched on in this thread Why angles have units since they are defined by a ratio of distances?

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