Why are there 2 pi radians in a circle?

Abraham Banks

Abraham Banks

Answered question

2023-01-01

Why are there 2 pi radians in a circle?

Answer & Explanation

ExcendLicceneixi

ExcendLicceneixi

Beginner2023-01-02Added 11 answers

According to one definition, when theta is placed in the center of a circle with radius r, the ratio of the arc length s to radius r is the radian measure of the angle theta. The angle that runs once around the circle has a radian measure of C/r=2r/r=2, as the diameter of the whole circle is equal to its arc length, 2r. As long as we measure theta in radians, we may use the formula for arc length s=rtheta because of this definition. Whatever unit is chosen to measure r and s, it should be noted that they cancel out in the definition of radian measure. We refer to radian measurement as being dimesionless. Also take note of the fact that some instructors may introduce the radian measure without going through its 'official' meaning as a ratio of lengths.
They only state that there are two radians after going around the circle. (Some claim that 2 radians are equivalent to 360 degrees.) This gives the impression that it is arbitrary when it actually is not.

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