Convertion of radian to degree question!?

Question

pi/12 (180/pi) = 15 (degrees)

How did they get 15?

Answer 1

180 / 12 = 15

Answer 2

I will solve this without a calculator.

Let R = radians and D = degrees

To convert from degress to radians:
R = Dpi/180

To go the other way, do some quick work such as:
R = Dpi/180 <=> 180R = Dpi
<=> (180R)/pi = D
<=> D = (180R)/pi

=> D = (180R)/pi

Now,
Let R = pi/12

=> D = [180(pi/12)]/pi
<=> D = (180pi)/(12pi)
<=> D = 180/12
<=> D = (10*18)/(3*4)
<=> D = (2*5*9*2)/(3*2*2)
<=> D = (2*5*3*3*2)/(3*2*2)
<=> D = (2*2*3*3*5)/(2*2*3)
<=> D = (3*5)
<=> D = 15

=> R = pi/12 <=> D = 15

Answer 3

Best way is to remember one relationship and then always use proportion. Example:

pi = 180 degrees

Therefore, to convert 15 degrees to radians:

15/180 * pi = pi/12 radians

To convert pi/12 radians to degrees:

(pi/12)/pi * 180 = 180/12 = 15 degrees.

Answer 4

in your question, you can just cancel out the two pi's so that leaves you 18/12 which is 15.

In general, 1 pi radians is equal to 180 degrees. So you do your conversions based on that.

Answer 5

pi radians = 180 degrees
pi/180 radians = 1 degree

so to convert degrees to radians, multipy by pi/180

15 degrees = 15*(pi/180) radians = pi/12 radians

Answer 6

pi/pi=1,
so (1x180)/12=15
=)

Answer 7

(pi/12)(180/pi)
(180pi)/(12pi)
(180/12)
15

Answer 8

see page 297