question about converting Rads to degrees?

Rhino

So I understand rads is they are in the form of x*PI / y

That is pi/3 = 60 degrees.

My book sometimes just has "4.7". There is no degree sign, so assume this is rad.

4.7 what? 4.7 times 2pi? 4.7 pi?

How many degrees is 4.7? In terms of pi, how many rads?

msuitepyon

Converting to radians from degrees --> multiply by pi/180
Converting to degrees from radians --> multiply by 180/pi

Assuming 4.7 is in radians (which it sounds like it is), that would equat to roughly 269 degrees because 4.7 * (180 / pi) = 269.290164.

msuitepyon

Also a quick lesson in dimensional analysis! I hated this at times, but damn it if it doesn't help.

Say you're trying to find something--for example, the degree measurement of a angle given in radians. Let's say 4.7 radians. What's that in degrees?

If you look at my conversion factor above, to go to degrees from radians to multiply by 180/pi. In this sense, 180 is a measure of degrees and its equivalent is a measure of radians (because pi radians is 180 degrees, right?). You started off with radians and when you multiply by degrees/radians you should get degrees. If you don't, something's wrong.

(radians / 1) * (degrees / radians) = degrees

You divide radians by radians to get 1 and you're left with degrees.

Dimensional analysis is a little extra step to make sure you're not crazy and your formula is correct.

japan

Radians don't have to be expressed in terms of Pi, it's just sometimes more convenient (and often more accurate) to do so.

So your 4.7 is just 4.7 radians, convert as you normally would. Given that you know 360 degrees = 2pi radians, 1 radian = 180/pi degrees

Syphyre

msuitepyon is spot on. If you've having trouble mentally setting yourself up, this picture can help too. http://math.rice.edu/~pcmi/sphere/degrad.gif

Also, something I tripped up on when I was in school, Pi is not a unit of measurement. So it's not 2.3 "pi-radians" Pi is just a (extremely helpful) constant. So 2.3pi radians. Replace pi with any other constant. Pi is just seen all the time because it makes the unit circle come out even.

Infidel

What often causes confusion is that you may say "4.7 radians" and from previous experience assume radians is some form of dimension.

It is not.

When you have "5m" you know you're talking about a length. "X radians" or "Y degrees" is not a dimension, it is a pure ratio. Meters per meters = m / m = dimensionless.

The reason we need to distinguish them is because we have two conventions for representing the angle, radians and degrees, and 3 radians is very much different from 3 degrees, so the number alone isn't always enough. (Most of the time it is implied though.)

Dr. Math wrote:

Angles are indeed dimensionless; the reason is that an angle is
measured as the ratio of arc length to radius (meters per meter, say),
which cancels out any units. Other angle measurements, such as
degrees, are also dimensionless, though they are defined by different
ratios, such as the ratio of the arc length to 1/360 of a circle,
which results in the need for a multiplier. It is for this reason that
we still need to name the unit, radians, rather than leaving it out
entirely. Saying "radians" specifies the way in which the angle is
measured; but it is still dimensionless and can be ignored as long as
you know that radians are the correct method for the calculation being
done.

Rhino

delete

Rhino

msuitepyon wrote:

Converting to radians from degrees --> multiply by pi/180
Converting to degrees from radians --> multiply by 180/pi

Assuming 4.7 is in radians (which it sounds like it is), that would equat to roughly 269 degrees because 4.7 * (180 / pi) = 269.290164.

How do you subtract 4.7 from 3pi/2 without rounding? Book/online says exact answer in terms of pi.

3pi/2 - 4.7 =

3pi/2 - 9.4/2 =

(3pi)-9.4 /2 =

how do reduce? online course doesn't accept that answer. Says it needs to be a reduce fraction in terms of pi (says, error: not simplified).

If i convert/round to decimal it says to give exact answer in terms of pi (says: error: needs to be a reduced fraction in terms of pi)

edit: for decimal I get apox: 0.01238898038468985769396507491925
Is that part right at least?

Infidel

That result looks right. pi is just a number and so you multiply by 3 and subtract a number from a number. All dimensionless.

Veevee

Have you tried asking your teacher these questions? I'm betting he'll be more helpful for this specific question (how to convert while also entering into an online form) than we could