# Math Help - Why differentiation and integration is impossible with angle expressed in degrees?

1. ## Why differentiation and integration is impossible with angle expressed in degrees?

Why is differentiation and integration impossible with the angle expressed in degrees? Why the angle have to be expressed in radians?
I have wondered about this my whole... time doing those differentiations and integrations

2. Originally Posted by ssadi
Why is differentiation and integration impossible with the angle expressed in degrees? Why the angle have to be expressed in radians?
I have wondered about this my whole... time doing those differentiations and integrations
Why do you think it's impossible? It's not.

3. Originally Posted by mr fantastic
Why do you think it's impossible? It's not.
Why do then the calculators have to be fed with angles in radians in order to calculate the differentiation and integration results properly?

4. Originally Posted by ssadi
Why do then the calculators have to be fed with angles in radians in order to calculate the differentiation and integration results properly?
They don't.

5. Originally Posted by mr fantastic
They don't.
But they do display certain evidences that suggest they have gone berserk when I the angles are in degrees.

6. Originally Posted by ssadi
Why is differentiation and integration impossible with the angle expressed in degrees? Why the angle have to be expressed in radians?
Radians are real numbers. I am not sure what a degree is.
One radian is the measure of any central angle of a circle that subtends an arc of length equal to the radius of the circle.

7. Originally Posted by Plato
Radians are real numbers. I am not sure what a degree is.
One radian is the measure of any central angle of a circle that subtends an arc of length equal to the radius of the circle.
I know the definition of radian. But that does not help much.
I found the explanation in wikipedia
Somebody out there must understand the stuff better, all it succeded to do was leaving my eyes sore.
But I really wanna understand...
Why is the derivative of sin(x) only cos(x) when x is measured in radians? Algebra man 18:56, 18 March 2007 (UTC)
• The derivative of a function f at a point x is the ratio of a small displacement in input from x divided into the resulting small displacement in output from f(x).
• Therefore sin(2x) will have a derivative twice as large as sin(x), for example; and in general the derivative will depend on the units of input. (This is true for any non-constant function.)
• At x = 0, cos(x) is exactly 1 no matter what input units we use.
• Therefore we can have only one possible choice of input unit for the sine function if its derivative is to match.
• Radian measure (arc length) works, as shown by a geometric argument.
• Therefore radian measure is the unique measure permitting the derivative of sin(x) to be cos(x').

This line of reasoning does not prove that the correspondence holds for all values of x, but it does show that if it is to hold at all, we must use radians. (I assume that anyone who could handle the general proof wouldn't be asking this question.) --KSmrqT 23:36, 19 March 2007 (UTC)