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July 7th, 2019, 02:37 PM   #1
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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.
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July 7th, 2019, 04:28 PM   #2
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Originally Posted by NineDivines View Post
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
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Last edited by skipjack; July 7th, 2019 at 06:09 PM.
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July 8th, 2019, 06:40 PM   #3
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Why angles have units since they are defined by a ratio of distances?
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