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.

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

Doc Al
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.

Ray Vickson
Homework Helper
Dearly Missed
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

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.

Ray Vickson
Homework Helper
Dearly Missed
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

eumyang
Homework Helper
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:
$\frac{2\pi \text{ rad}}{57.296 \text{ deg}} \approx \frac{0.110 \text{ rad}}{1 \text{ deg}}$

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Doc Al
Mentor
This looks like a proportion to me. If it was written like this:
$\frac{2\pi \text{ rad}}{1 \text{ rad}} \approx \frac{0.110 \text{ deg}}{1 \text{ deg}}$
... then it would make more sense to me.
Why would that make more sense? (Those ratios aren't even close.)

eumyang
Homework Helper
Typo. Fixed.

Doc Al
Mentor
That's more like it.

SteamKing
Staff Emeritus