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The natural unit for measuring angles is the radian, which is derived from the formula for
the circumference c of a circle: c = 2 π × r, where r is the radius. If r = 1, then c = 2 π,
so the radian is defined such that a circle has 2 π radians. It also has 360 degrees.
1 radian = 360 / 2 π = 180 / π =57.295779513082320876798154814106 degrees
1 degree = 0.017453292519943295769236907684886 radians
1 arcmin = 0.000290888208665722 radians
1 arcsec = 0.00000484813681109536 radians.
Angle | Degrees | Part of Pi | in numbers |
90° | π/2 | 1.570796327 | |
60° | π/3 | 1.047197551 | |
45° | π/4 | 0.785398163 | |
30° | π/6 | 0.523598775 |
Formulas
Conversion from radians (RAD) to degrees (DEG):
DEG = RAD × 180 / π ~ 57.296 × RAD
Conversion from degrees (DEG) to radians (RAD):
RAD = DEG × π / 180 ~ 0.01745 × DEG
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