# Homework Help: Degree radian conversion issue

1. Jul 17, 2011

### xzi86

Not really a standard question, just need some clarification.

So I saw this in the textbook: 2pi/radian = 0.110/degree

What does this mean? Does it mean 2pi equals 0.110 degrees? But I don't think that's the case. I'm trying to find out the value of radians from this equation. Would you say in radians it's 2pi? Sorry I'm very confused on this especially by the / sign. Any help would be appreciated. Thanks.

2. Jul 17, 2011

### GreenPrint

pi = 180 degrees
1 = (180 degrees)/pi

3. Jul 17, 2011

### Staff: Mentor

I don't quite understand that equation, but all you need to convert back and forth between radians and degrees is 2pi radians = 360 degrees.

4. Jul 17, 2011

### Ray Vickson

pi radians = 180 degrees, so (for example) 40 degrees = (40/180)*pi radians, and 3 radians = (3/pi)* 180 degrees. Note that pi is NOT 22/7, or 3.14 or anything simple like that. However, in most everyday applications the *approximation* pi ~3.1413 is good enough.

RGV

5. Jul 17, 2011

### GreenPrint

Yes, and if you were to estimate use 355/113. 355/113 is about 3.14593 or pi rounded off after five digits out from the decimal point. 355/113 is a much better approximation than 22/7, which is only accurate to two digits out from the decimal point.

6. Jul 17, 2011

### Ray Vickson

Sorry: there is a typo in the above. I should have said pi~3.1416 (or 3.14159 or 3.141593 or 3.1415926 or .... )

RGV

7. Jul 17, 2011

### eumyang

This looks like a proportion to me. Maybe it's supposed to be written like this?
$\frac{2\pi \text{ rad}}{1 \text{ rad}} \approx \frac{0.110 \text{ rad}}{1 \text{ deg}}$

Though the units are mixed up. This would be better:
$\frac{2\pi \text{ rad}}{57.296 \text{ deg}} \approx \frac{0.110 \text{ rad}}{1 \text{ deg}}$

Last edited: Jul 17, 2011
8. Jul 17, 2011

### Staff: Mentor

Why would that make more sense? (Those ratios aren't even close.)

9. Jul 17, 2011

### eumyang

Typo. Fixed.

10. Jul 17, 2011

### Staff: Mentor

That's more like it.

11. Jul 17, 2011

### SteamKing

Staff Emeritus
The solution to your problem is to throw that book away. There is no telling what other mistakes it contains.