Why is the circular function tangent with an argument of 90° undefined? If it is defined then its value would be infinity. However, infinity could never be a number since it cannot be operated mathematically: it cannot be added, multiplied, subtracted, nor divided.

On the other hand, the circular function sine with argument of 90° equals unity and the circular function cosine with 90° argument equals zero. Furthermore, tangent 90° is defined as the ratio of sine 90° over cosine 90° but division by zero is forbidden in mathematics. This is why tangent 90° is still undefined. In number of years, tangent 89.999999999° is approximately the age of the universe according to the big bang theory. This is easily verified by using a simple handheld electronic pocket calculator. Using radian angular measurements, the same can be achieved if the argument is p/2.00000000009.