4 ms·
To be fair, thse functions aren't defined for physical quantities. As a physicist, if you ever see units on the parameter to a trigonmetric function, you can b
by marginalia_nu 3y ago
To be fair, thse functions aren't defined for physical quantities.
As a physicist, if you ever see units on the parameter to a trigonmetric function, you can be fairly certain something is wrong.
You can derive this from how e.g. cos(x) can be written as a polynomial series, something like 1 - x^2 + whatever; and since 1 and x^2 would have different units if x is anything but unitless, you've goofed.
That's a big reason why units are used in calculations in the first place. They basically act as a sort of checksum for your calculations.
- sharkdp 3y ago> As a physicist, if you ever see units on the parameter to a trigonmetric function, you can be fairly certain something is wrong. Exactly. Which is why trigonometric functions in Numbat have the signature cos(x: Scalar) -> Scalar and only take quantities as arguments that are implicitly convertible to a scalar, like 'cos(pi / 3)', 'cos(30 deg)' or 'cos(0.5 turn)'. Whether or not angles should be considered dimensionless is actually a matter of academic dispute. If you want to know more, take a look at https://github.com/sharkdp/numbat/pull/167 https://github.com/sharkdp/numbat/pull/167 and the references therein.
- pklausler 3y agoRadians vs degrees?
- mikewarot 3y agoRadians, gradians, degrees, minutes, seconds, thirds, revolutions are all ways of dividing up a circle
- marginalia_nu 3y agoFor radians, we can note that the length of a circle segment is rα, where r is the radius and α is the angle, where both the radius and circle segment have dimensions length; then we must infer that α is dimensionless. Degrees follow a similar argument.