say I have something like ( 7° 11' 22" )^2 or ( 7° 11' 22" )^0.5 would this be undefined?
Thanks for the reply. What I'm trying to get at is what happens to the units. If I take the unit inch and square it I have an area, and it I cube it I have a volume. But what do I have if I take an unit of angle and raise it to a power, be it 2, 3, or 1/2? what sort of meaning does the output unit have? I think that it maybe undefined. . .
Right, I understand that radians are unitless. Maybe it would help if I described exactly what I'm, trying to do (sorry I did not outline it clearly in the first post). I'm writing a program to handle the sexagesimal system with ease and with an intuitive user interface. It will also have modes for radians and decimal degrees. So all is well until I start thinking about what happens when the user is in the sexagesimal system and enters (7° 11' 22")/(7° 11' 22"), not so bad the solution is 1 with out units. But what happens when the user asks for (7° 11' 22")(7° 11' 22"), not so easy because now I have squared angler units. Does a squared angler units have a definition? What happens when the user asks for (7° 11' 22")^2 or (7° 11' 22")^(1/2)? So I'm thinking that I should return the message "Invalid Input" or "undefined" in such cases, but I want to be absolutely positive that I have it right. FYI when I ask my Texas Instrument for (4°)^2 it returns 16, but I'm still skeptical.
Thanks for any help
Actually there is such a thing as a "square degree" - it's a unit for a solid angle representing how much of a sphere an object occupies. Astronomers often talk in terms of how much sky an object fills, using this solid angle measurement system. Couple of sites that might be helpful:
Square degree - Wikipedia, the free encyclopedia
Steradian
There are 60 minutes in a degree and 60 seconds in minute. Therefore, there are $\displaystyle 60^2= 3600$ "square minutes" in a "square degree" and 3600 "square seconds" in a "square minute". $\displaystyle 22^2= 484$ which is less than 3600 and $\displaystyle 11^2= 121$ which is less than 3600. $\displaystyle 7^2= 49$ of course so "7 degrees 11 minutes 22 seconds" squared is 49 square degrees, 121 square minutes, 484 square seconds.
As for the square root of it, I would agree with Prove It that you would be better of writing 11/60= .183333... degrees and that 22/3600= .006111... degrees so that the "square root of 7 degrees 11 minutes 22 second" is the square root of 7+ .183333+ .0061111= 7.1894444... degrees so you could take the square root of that.
Thank you everyone for replying!
@skeeter - the program does change all units into radians before any operation as all computer languages that I know of want radians for sin, cos, etc. Then the program changes it back into DMS for output.
@HallsofIvy - I understand the how to square and square root the angle values, the question is does the output of the operation have any meaning. e.g. if I have (30° F)^{2} what is the meaning of the unit °F^{2}? Not much. It does not associate with any thing in "physical space." It seems to me that the angle units raised to powers (other then 1) is a similar "non-thing", save the case of the solid angle pointed out by ebaines.
@ebaines - Thank you for the info on the solid angles. Looks like this may be the only example of raising an angle to a power. . .
I think that I'm getting closer to saying that multiplication operation on the arguments 7° and say 4° will result in a meaningless solution and therefor should not be valid input from the user. And the same for powers save the solid angle case. If any one disagrees please let me know.
Again thanks for all the feed back.