Question

57.2957795131 = 1 rad
How to calculate this? What is the fraction?

Answer 1

what do you mean?

Answer 2

hint: there are pi radians in 180 degrees

Answer 3

ok, let me rephrase, 1 rad = 180/pi which is approximately 57.2957795131
so if i calculate this by hand, how do i know what pi is? So 180 devided by what?

Answer 4

Pi is transcendental, with digits that go on forever, with no pattern
http://www.piday.org/million.php/

Answer 5

well it depends on how many decimal places of a radian you want it accurate to
you have quoted 10 places so you need pi accurate to 11 places

Answer 6

yes - i believe they know now pi to 100 million places - maybe more!

Answer 7

ok, not exactly the answers im looking for but thanks for these answers. Let me give an example:

120 degrees = 120 * pi/180 = 2pi/3 rad

how do i calculate this without a calculator? How do I know what pi is in order to do the calculation?

Answer 8

generally people leave radians in terms of pi (because there is no exact value of pi in decimal or rational form)

if you insist on changing to a decimal value, use pi to the accuracy required by the problem.

Answer 9

you will notice that angle measures in radians often have a pi in them.

Answer 10

ok, thanks, so it is easier to leave the answer with pi in them.

Answer 11

yes

Answer 12

\[\frac{180°}{\pi }\approx \frac{180}{22/7}=\frac{180\times 7}{22}\]\[=\frac{2^2\times3^2\times5\times7}{2\times11}=\frac {2\times3^2\times5\times7}{11}\]\[=\frac{630}{11}=
\frac{660}{11}-\frac{30}{11}\]\[=60-\frac{30}{11}\]\[= 60-\frac{33}{11}+\frac 3 {11}\]\[\quad =57+\frac{3}{11}\]