Tangent of 90 Degrees

Date: 5/24/96 at 13:28:26
From: Anonymous
Subject: Trignometry

Why is the tangent of 90 degrees "no solution"?

Date: 5/28/96 at 20:24:37
From: Doctor Pete
Subject: Re:Trignometry

There are lots of ways to think about why tan(90) is not defined.  You 
can go by the book:  tan(x)=sin(x)/cos(x), but since sin(90)=1 and 
cos(90)=0, and division by 0 is not allowed, tan(90) has no meaning.

Or think about it geometrically:  say we have a right triangle ABC, 
with angle ACB=90.  Then look at, say, angle BAC.  tan(BAC) = BC/AC, 
but BAC is less than 90 degrees.  We can make angle BAC closer and 
closer to 90 degrees by increasing the length of BC, but as we keep 
doing this, AC stays the same so the ratio BC/AC gets infinitely 
large.  So tan(90) has no geometric meaning.  (Draw a picture, it'll 
help a lot.)

-Doctor Pete,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/