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
_____________________________________________

Terminal Side


Date: 04/21/97 at 17:07:21
From: Laura
Subject: sin/cosin

Find cos(A) if the point (2,-3) is on the terminal side of A.
I am totally stuck and I have no idea how to even begin!


Date: 04/27/97 at 01:14:41
From: Doctor Mike
Subject: Re: sin/cosin

Dear Laura,
  
I'm going to have to try to draw a picture for this. Sorry if the 
picture is not great.   The "terminal" side is the hypotenuse of the 
triangle.  The "initial" side is the triangle leg that goes from the 
origin along the positive x-axis direction. 

                           +y
                            ^
                          +1|
                            |
          -2      -1        |       +1       +2
   -x <---*--------*--------+--------*--------*------> +x
                            |\  A             |
                            |  \              |
                          -1|    \            |
                            |      \          |
                            |        \        | -3 
                          -2|          \      |
                            |            \    |
                            |              \  |
                          -3|                \|
                            |                  (+2,-3) 
    
Now, by the Pythagorean theorem, since the lengths of the two legs of 
this right triangle are 2 and 3, you find the length of the hypotenuse 
by taking the square root of 2^2 + 3^2 = 4+9 = 13. So, the hypotenuse 
length is sqrt(13). Note that I have labelled the vertical leg "-3" 
because it is going downwards from the x-axis.     
   
Now, with all this set-up your question is easy. The cos(A) is the 
"adjacent" over "hypotenuse," or +2/sqrt(13). If you want to get rid 
of the square root in the denominator, multiply both numerator and 
denominator by sqrt(13), like the following: 
   
            +2        sqrt(13)        2*sqrt(13)
        ---------- * ----------  =  -------------      
         sqrt(13)     sqrt(13)            13     
    
I hope this helps. Now do the same for sin(A) and tan(A)!   
     
-Doctor Mike,  The Math Forum
 Check out our web site!  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/