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### 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/
```
Associated Topics:
High School Euclidean/Plane Geometry
High School Geometry
High School Trigonometry

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