I have learned about the correspondence of radians and degrees so 360° degrees equals 2π radians. Now we mostly use radians (integrals and so on)
My question: Is it just mathematical convention that radians are much more used in higher maths than degrees or do radians have some intrinsic advantage over degrees?
For me personally it doesn’t matter if I write \cos(360°) or \cos(2\pi). Both equals 1, so why bother with two conventions?
Answer
The reasons are mostly the same as the fact that we usually use base e exponentiation and logarithm. Radians are simply the natural units for measuring angles.
- The length of a circle segment is x\cdot r, where x is the measure and r is the radius, instead of x\cdot r\cdot \pi/180.
- The power series for sine is simply \sin(x)=\sum_{i=0}^\infty(-1)^i{x}^{2i+1}/(2i+1)!, not \sin(x)=\sum_{i=0}^\infty(-1)^i(x\cdot \pi/180)^{2i+1}/(2i+1)!.
- The differential equation \sin (and \cos) satisfies is f+f”=0, not f+f”\pi^2/(180)^2=0.
- \sin’=\cos, not \cos\cdot 180/\pi.
You could add more and more to the list, but I think the point is clear.
Attribution
Source : Link , Question Author : Slater , Answer Author : tomasz
