B Are trigonometric ratios physical quantities?

[Suyogya]

I already know the fact that angles are physical quantities, but sin, cos of some angles are quantities?
Quantities are those things, which can be quantified, are sin, cos, tan be quantified through measurement, if yes then other mathematical functions should also be categorised as physical quantities, but they not, why?

 

[phinds]

I already know the fact that angles are physical quantities ...

Well, not really. Angles are DESCRIPTIONS of physical attributes, as are other math functions such as the trig functions.

 

[Suyogya]

Well, not really. Angles are DESCRIPTIONS of physical attributes, as are other math functions such as the trig functions.

Angles are physical quantities (as written in the Wikipedia's list of derived quantities)

 

[fresh_42]

Angles are physical quantities (as written in the Wikipedia's list of derived quantities)

This distinction leads nowhere. E.g. take the angle of reflection on a mirror: is it a physical quantity or the description of what the light beam does? That's a question for linguists and philosophers. You defined a physical quantity of something, that can be measured. O.k., that makes sense as quantity already implies a measurement. But what did you have in mind as a mathematical function, that can be measured and does not correspond to a physical quantity?

You must always make the step from mathematics to physics beforehand, which is why @phinds called it a description. A mathematical function is nothing but a set of pairs. So before you can call it a physical quantity, you have to say, what these pairs should describe! It's not the pairs that can be measured, it's their identification with a real word property. Wikipedia wasn't accurate here, because the goal of that page wasn't a philosophical one, but a practical one. In any case, this transformation step from mathematics to physics has to be made, even if you hide it somewhere, as e.g. in distance (value of a metric) equals length (measurable physical quantity).