how do you convert radians "in decimal form" to degrees?
I know you can do like
2pi rads = 2pi*180/pi cancel the pi's and you got 360 degrees as an answer.

But I wrote a test and a question was find the angle theta with radius 16cm and arc 32cm ****(this is what threw me off, I thought it had to be like 16cm(pi) or something)*****

so I used the formula the formula

theta=a/r and got 2 radians (not 2pi)

so I tried to put this into the formula to convert to degrees and got 360/pi????
THis was on a no calculator part of the exam so I got stuck, and thought it might have been like a trick question so the only thing I could think of was that thats 360/pi = 2pi/pi = 2degrees which cant be right because radians cant be equal to the degrees????

thank you.

2. Radii and other measures of length can be in any form of number (other than complex or negative values) and can have any unit of measure (as long as it's a measure of length, rather than volume or something). There is no requirement that a radius be stated in terms of $\displaystyle \pi$.

When no calculator is allowed, they should not, in my opinion, be wasting your time asking you to do the long division of 360 by the decimal approximation 3.14 (or whatever value they'd specified) to convert the angle measure to degrees.

But that's the way you'd do the conversion: Divide 360 by 3.14:

Code:
long division:
114
------
314 )36000
314
------
4600
314
------
1460
1256
------
204
So you've got $\displaystyle 114\frac{102}{157}^\circ$.

Whether or not you want to continue on to get the decimal degrees or else the "minutes" and "seconds" is up to you.

3. Ya I dont know every other time we did this the arc length was given as something with pi like 7pi cm I think.

so we got something like theta = pi/6 radians so pi cancled and we got degrees, or it we were allowed to use calculators and give a decimal answer.

This was no calculator and multiple choice. we had a 30 minute time limit so I dont see why they would make us do long division.

thank you.

4. If it was multiple choice, maybe they expected you to estimate...? And then pick the "obvious" choice from the listed options...?

5. Originally Posted by stapel
If it was multiple choice, maybe they expected you to estimate...? And then pick the "obvious" choice from the listed options...?
It is also possible that they wanted you to leave it in terms of pi