Error in Computing Undefined

[Joe Horn]

It's not a bug or even a problem. It's actually the correct answer. Here's why.

In Home view (not CAS), with Standard display mode set, type pi/2 and see what you get. It says 1.5707963268 and it's very important to know that it's EXACTLY 1.5707963268, no more and no less. It's NOT pi/2, but an approximation of pi/2, rounded to 12 significant digits. Therefore, when you key TAN(pi/2), you're REALLY asking for the tangent of 1.5707963268, not the tangent of pi/2. As verified by a computer, TAN(1.5707963268) is -195948537905.97787... which, when rounded to 12 significant digits, is -195948537906, which is precisely what Prime returned.

The reason that TAN(90°) returns infinity is that 90° is an exact value. In Home, pi/2 is not exactly pi/2.

If you want to calculate with the exact value of pi, use CAS instead of Home. You'll notice that tan(pi/2) nicely returns infinity, as expected.