## FANDOM

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Radians are another way to measure angles, where 1 radian is defined as the π/2th of a right angle. The definition of radians is less arbitrary than the definition of degrees because on a θ-radian arc on a circle with radius 1, the arc length is equal to θ. Since there are π radians in a half of a circle (180˚), there are 180/π = 57.2958... degrees in a radian. This number could be thought as a number linking an arbitrary measure (degrees) to a non-arbitrary measure (radians).

I read on a forum post that given a large number, you can make a larger number by taking the reciprocal of it, subtracting it from 90, and taking the tangent of it (in degrees). In other words, given a number n, tan((90-1/n)˚) is a larger number. For example, doing it on 100 gives tan(89.99˚) = 5729.577... However, the result is always smaller than (180/π)*n, which is smaller than 58n. So if the number n is large enough, this method won't be very effective in generating larger numbers.

This also holds on units other than degrees. In a unit where a right angle is equal to x units, doing this procedure (replacing 90 with x) will result in a number smaller than 2x/π times the number. In particular, if you did this in radians (where x = π/2), the result will be actually smaller than n (or almost exactly the same if n is large enough).

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