# 'New' type of angle measurement to often replace radians

1. Sep 3, 2010

### Twinbee

Maybe I'm biased because of the kind of projects I'm pursuing (raytracing), but I can't help feeling that for many areas, instead of defining a circle in terms of radians (or degrees for that matter), we should simply use unity and define say, a quarter of a circle as being 0.25.

Obviously a radian has the same length as the radius of a given circle, and I understand that radians have their place (for example, angular velocity in physics), and can help to reduce the number of unnecessary factors. But for other projects, defining angles from zero to one can also help reduce the factors.

Because of the above I'm ending up defining my own trig commands, e.g.:
MySin(0.125) = 0.7071... (1/8th of a circle)
MySin(0.25) = 1... (1/4th of a circle)
etc.

Has anyone else found this could be useful or is it just me?

Last edited: Sep 3, 2010
2. Sep 3, 2010

### Office_Shredder

Staff Emeritus
You lose all the nice calculus results like this

3. Sep 3, 2010

### HallsofIvy

However, as Office Shredder says, calculus formulas like d(sin(x))/dx= cos(x), d(cos(x))/dx= - sin(x), $\int sin(x)dx= -cos(x)+ C$, $\int cos(x) dx= sin(x)+ C$ are only true for x measured in radians.

4. Sep 3, 2010

### Office_Shredder

Staff Emeritus
I thought a grad was 1/400th of a circle

5. Sep 3, 2010

### Redbelly98

Staff Emeritus
This is not a new idea, many people do use a complete revolution as the unit of an angle. Do you know what "rpm" and "Hz" stand for?

6. Sep 3, 2010

### Twinbee

@Redbelly98: Yes, but I never see any calculators use 'revs' or 'cycles' in addition to degrees or radians, for use in trigonometric functions. That seems pretty strange because as you said, they're used everywhere. So I need to define the functions separately (which the excellent CCalc (console calculator) for example allows one to do thankfully).

Just to clarify, I'm certainly not advocating that we completely replace radians (for the reasons given in the above posts). I'm on the fence about using 'my' system as default, but my bias could certainly be affecting that particular judgment. I just think that using it in addition to the other two popular systems would be very useful.

Again, is there anyone other than me who would find revs instead of radians more useful for their everyday math/sciency stuff?

Last edited: Sep 3, 2010
7. Sep 4, 2010

### HallsofIvy

You are right- I mispoke. There are 100 grads to a right angle. That way engineers can think of grades as "percentages".

What I should have said was "4 of your measures = 100 grads= 90 degrees= pi/2 radian." so that 1 of this "new measure" is 25 grads= 22.5 degrees= \pi/8 radians.

8. Sep 4, 2010

### HallsofIvy

Wave frequency is typically given in terms of "Herz" and, of course, automotive engineers and mechanics often use "rpm".

9. Sep 4, 2010

### Redbelly98

Staff Emeritus
And then there was the advice my thesis advisor gave me, "When you open up a valve in a vacuum system all the way, be sure to back it off a quarter of a turn so that the threads don't seize up over time."

We also would refer to motions of adjustment screws as "2 turns", "half a turn", etc.

EDIT: I vaguely remember, while I was working out numerical solutions to a DC motor's motion a couple of years ago, that I was using revolutions. But that might have been simply a conversion of the output, after letting the code work things out in radians first.

Last edited: Sep 4, 2010