yep, I don’t think the question “what’s the cos of a unit” is valid because cos expects a plane angle in the input and a unit doesn’t meet that expectation; it’s underdefined; it depends whether the calculator is set to radians or degrees.
It’s not undefined.
You cannot take the exponential of anything with dimensions. That also applied to logs and trigonometric functions. Ergo, angles must be unitless.
I understand that the taylor series used to define sin and cos is a function with a unitless input but practically, a lot of people like to use degrees for the input of sin and cos instead. I hate that it’s ambiguous, because calculator software devs use it as an excuse to misrepresent physical quantities like angular velocity, frequency, torque, etc.
Also, it’s very valuable to be flexible with the count of base units defined in the system. A lot of software is written with three (length, mass, time), some with 7 (as in SI), and I want to be able to shove in angle as a base unit in anywhere.
Angular velocity can be given in rad/s. No one will bat an eye if you do that. It’s even recommended. But it’s not a unit in the same sense than the other ones.
but I’m the user, I want the definitions to cater to me and describe my world. I want my definitions-based logic to make sense. And if torque is defined as joules but shows up as J/rad in the UI, then who supplies the /rad except an additional definition for a contradiction or exception? My conclusion from that is that the definition is missing something shaped like a base dimension for angle.
You disagree that a ratio is unitless? What’s the cos of a unit?
yep, I don’t think the question “what’s the cos of a unit” is valid because cos expects a plane angle in the input and a unit doesn’t meet that expectation; it’s underdefined; it depends whether the calculator is set to radians or degrees.
It’s not undefined. You cannot take the exponential of anything with dimensions. That also applied to logs and trigonometric functions. Ergo, angles must be unitless.
I understand that the taylor series used to define sin and cos is a function with a unitless input but practically, a lot of people like to use degrees for the input of sin and cos instead. I hate that it’s ambiguous, because calculator software devs use it as an excuse to misrepresent physical quantities like angular velocity, frequency, torque, etc.
Also, it’s very valuable to be flexible with the count of base units defined in the system. A lot of software is written with three (length, mass, time), some with 7 (as in SI), and I want to be able to shove in angle as a base unit in anywhere.
You’re conflating UI and definitions.
Angular velocity can be given in rad/s. No one will bat an eye if you do that. It’s even recommended. But it’s not a unit in the same sense than the other ones.
but I’m the user, I want the definitions to cater to me and describe my world. I want my definitions-based logic to make sense. And if torque is defined as joules but shows up as J/rad in the UI, then who supplies the /rad except an additional definition for a contradiction or exception? My conclusion from that is that the definition is missing something shaped like a base dimension for angle.