57.2957795131 = 1 rad How to calculate this? What is the fraction?
what do you mean?
hint: there are pi radians in 180 degrees
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?
Pi is transcendental, with digits that go on forever, with no pattern http://www.piday.org/million.php/
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
yes - i believe they know now pi to 100 million places - maybe more!
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?
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.
you will notice that angle measures in radians often have a pi in them.
ok, thanks, so it is easier to leave the answer with pi in them.
yes
\[\frac{180°}{\pi }\approx \frac{180}{22/7}=\frac{180\times 7}{22}\]\[=\frac{2^2\times3^2\times5\times7}{2\times11}=\frac {2\times3^2\times5\times7}{11}\]\[=\frac{630}{11}= \frac{660}{11}-\frac{30}{11}\]\[=60-\frac{30}{11}\]\[= 60-\frac{33}{11}+\frac 3 {11}\]\[\quad =57+\frac{3}{11}\]
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