# How To Map Infinity To It's Reciprocal Using Trigonometry

Robert Washbourne - a year ago - math, science

A reciprocal of a number is the number over itself; for example, the reciprocal of 2 is 1/2, which equals 0.5. However, it is not always that simple. The reciprocal of infinity should be 0, because 1 is a finite number, and infinity is infinite. But if you put 1/infinity in your calculator and hit enter, it gives you a domain error.

But now, let’s do it using triangles.

Let K = opposite / adjacent in a triangle.

Opposite is Y (Y=X), adjacent is 1, and X is tangent of the angle. If we do arctan(x), we get the angle of the triangle. X is tangent of the angle, because bottom side is 1.

Now that we have atan(X) as an angle, if we do cot (cot is 1/tan(x)), we can get adjacent over opposite, which is the same as 1 / X. Thus, if we take cot ( atan ( X) ) = 1 / X.