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Mathematics 57 Online
OpenStudy (didee):

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

OpenStudy (lgbasallote):

what do you mean?

OpenStudy (cwrw238):

hint: there are pi radians in 180 degrees

OpenStudy (didee):

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?

OpenStudy (phi):

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

OpenStudy (cwrw238):

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

OpenStudy (cwrw238):

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

OpenStudy (didee):

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?

OpenStudy (phi):

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.

OpenStudy (phi):

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

OpenStudy (didee):

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

OpenStudy (cwrw238):

yes

OpenStudy (unklerhaukus):

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

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