Q: How can 1 radian be defined?

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The radian measure IS the arc length of the unit circle, by definition - that is how the radian is defined in the first place.

1 radian = 1/tau or 1/(2*pi) of a whole turn.

A radian is an arc of the circumference of a circle and it is about 57.3 degrees.

1 degree = pi*radian/180 So therefore 15 times pi*radian/180 = pi*radian/12

1 rotation/1 min * 1 min/60s * (2*Pi radian/1 rotation)

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The radian measure IS the arc length of the unit circle, by definition - that is how the radian is defined in the first place.

There is no "radian of a straight line", as far as I know. A radian is a unit of angular measurement - defined in such as way that a complete circle (also known as 360Â°) is equivalent to 2 x pi.

1 radian = 360/tau (or 180/pi) degrees.

1 radian = 1/tau or 1/(2*pi) of a whole turn.

1 degree = pi*radian/180 So therefore 15 times pi*radian/180 = pi*radian/12

A radian is an arc of the circumference of a circle and it is about 57.3 degrees.

1 revolution = 2 x pi radians. Therefore, 1 radian = 1 / (2 x pi) revolutions.

1 rotation/1 min * 1 min/60s * (2*Pi radian/1 rotation)

1 revolution = 2pi radians therefore; 1 radian = 1revolution/2 pi radians = 0.159154943 revolution

1 rad = 57.3°

It is the derived unit of plane angle and 1 radian = one full rotation/2π. Also, it is equal to 57.296°.

Cosine of 1 degree is about 0.999848. Cosine of 1 radian is about 0.540302.