What 57.295 degrees mean to you

Question

I've just calculated that one radian is equals 57.295.. degrees, does this degree have special property instead the fact that it is just a degree that define radian in degree

Have you tried looking at the Wikipedia page? – Toby Mak Apr 23 '19 at 13:34 — Toby Mak, Apr 23 '19 at 13:34
No, i've not. Thanks for your suggestion – Fellas21 Apr 23 '19 at 13:37 — Fellas21, Apr 23 '19 at 13:37

score 4 · Answer 1 · answered Apr 23 '19 at 13:31

$57.295\dots$ is the number that, when multiplied by $2\pi$, yields $360$. There is absolutely nothing "special" about this number.

The only "meaning" behind a degree is "one $360$-th of a full circle", while a radian means "one $2\pi$-th of a full circle". From these two things, it already follows that $2\pi\mathrm {radians} = 360\mathrm{degrees}$, or, dividing by $2\pi$, that $$1\mathrm{radian} = \frac{360}{2\pi}\mathrm{degrees}$$

Note that while $\pi$ is a number with a certain significance (and therefore, measuring in radians makes inherent sense), $360$ is a completely arbitrary number that we decided to use a long time ago (measuring in degrees is therefore just a matter of convention).

score 0 · Answer 2 · answered Apr 23 '19 at 13:30

0

Radians and degrees are defined so that $2\pi$ radians is $360$ degrees. So $1$ radian is precisely $\frac{180}{\pi}$ degrees, which is the number you see there.

answered Apr 23 '19 at 13:30

Tyler6

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What 57.295 degrees mean to you

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