Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Tan 90


Date: 07/10/98 at 00:13:51
From: David Chung
Subject: Math

Why is tan 90 undefined?


Date: 07/10/98 at 03:25:38
From: Doctor Floor
Subject: Re: Math

Hi David,

Thank you for sending your question to Dr. Math!

To see why tan 90 is undefined, we should look at the way the tangent 
is defined. In a triangle it is defined in the following way:


                  C
               *  *
            *     *
         *        *
      *alpha      *
    A*************B

When ABC is rectangular with the right angle at B, then 
tan(alpha) = BC/AB. But from the triangle definition we can't say a 
thing about alpha = 90, because then there is no triangle anymore. 

To solve this definition problem, mathematicians switched to the 
unit-circle definition:

Create a circle centered at a point A with radius 1. From A draw the 
legs of your angle alpha. You can do this in such a way that one leg 
goes horizontally to the right, where it meets the circle in a point 
B. The second leg is is drawn in such a way that the angle is upwards 
for positive values and downwards for negative ones. Draw the line 
tangent (!) to the circle through B. The second leg and the tangent 
line meet in a point, say E. Now tan(alpha) is defined as the length 
of BE.

        

Now it is clear that if alpha = 90 there is no intersection of the 
second leg and the tangent line, so that tan 90 is not defined. 

If you have a math question again, please send it to Dr. Math!

Best regards,

- Doctor Floor, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Trigonometry

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/