How do you evaluate #tan 90 #?

1 Answer
Nov 27, 2015

#tan90^@# is undefined.

Explanation:

http://www.coolmath.com/precalculus-review-calculus-intro/precalculus-trigonometry/28-the-unit-circle-01

Since the angle is #90^@#, there will be a unit circle instead of a special triangle. Any point at #90^@# can be described as (#0, y#). However, to make things easier to understand, we will use a radius of #1#, meaning the height (#y#) is also #1#. The point will be (#0, 1#).

#tan90^@=y/x#
#tan90^@=1/0#
#tan90^@=#undefined

#tan90^@# is undefined because you can't divide #1# by nothing.

This is like saying:

#1# divided by #0# is #color(red)? rArr color(red)?# multiplied by #0# is #1#

Nothing multiplied by #0# will give an answer of #1#, so the answer is undefined.