Tan (90) = undefined actually; sin(90 = 1 and cos(90) = 0. You can also explain tangent of an angle is by dividing opposite line by the neighbor line. So in this “right angle” case your neighbor line is simply equal to 0 and the opposite line is 1.
Thinking back then I almost failed 1 year in the high school 23 years ago because of trigonometry and now explaining things here…
P.S: any number / 0 is equal to; If you are physicist, it can be zero depending on the theory you are applying it. However, if you are a mathematician, it is undefined.