# what happens if raise an angle unit to a power?

• Sep 17th 2012, 10:09 PM
fallingdog
what happens if raise an angle unit to a power?
say I have something like ( 7° 11' 22" )^2 or ( 7° 11' 22" )^0.5 would this be undefined?
• Sep 17th 2012, 10:27 PM
Prove It
Re: what happens if raise an angle unit to a power?
You're better off writing your angle as a single fraction, as squaring fractions is easy...
• Sep 17th 2012, 10:49 PM
fallingdog
Re: what happens if raise an angle unit to a power?
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. . .
• Sep 18th 2012, 03:02 AM
skeeter
Re: what happens if raise an angle unit to a power?
this is one of the reasons radians are used for angle measure. since they are defined by a ratio of arc length to radius, they are unitless.
• Sep 18th 2012, 09:17 AM
fallingdog
Re: what happens if raise an angle unit to a power?
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
• Sep 18th 2012, 10:22 AM
skeeter
Re: what happens if raise an angle unit to a power?
• Sep 18th 2012, 10:41 AM
ebaines
Re: what happens if raise an angle unit to a power?
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
• Sep 18th 2012, 11:53 AM
HallsofIvy
Re: what happens if raise an angle unit to a power?
Quote:

Originally Posted by fallingdog
say I have something like ( 7° 11' 22" )^2 or ( 7° 11' 22" )^0.5 would this be undefined?

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.
• Sep 18th 2012, 04:50 PM
fallingdog
Re: what happens if raise an angle unit to a power?