Hello, I searched the forum and couldn't find this topic, so I'll try and describe my question.(adsbygoogle = window.adsbygoogle || []).push({});

I want to know why using radians work and while they are 'natural'. I think the key equation is...

lim x→0 (sin x) / x = 1

...because it makes the derivatives of trigonometric functions relatively simple.

I'm not looking for a proof of the above limit - I know it can be proved various ways.

What I want to know is why is works for radians. What property of radians satisfies this? Why does sin x ≈ x for small values?

(I was thinking it might have to do with the Taylor series, but that relies on differentiating the function, so it can't be assumed.)

I'm looking for an answer analogous to why the derivative of e^x = e^x (e.g. if you look at it as an infinite series, when you differentiate, the first time disappears, and each subsequent term becomes the one before it)

This has been bugging me for some time. Please ask if you need any more clarification about what it is I'm asking

Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Why do radians *work* in calculus and higher maths?

**Physics Forums | Science Articles, Homework Help, Discussion**