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Standard Angles


Date: 08/09/2001 at 11:12:01
From: Nagaraj
Subject: Standard angles

Why are 0, 30, 45, 60, and 90 degrees taken as standard angles in 
trigonometry? Why can't we take some other angles?


Date: 08/09/2001 at 12:24:04
From: Doctor Peterson
Subject: Re: Standard angles

Hi, Nagaraj.

Mathematicians like to work with whatever is easiest. All of these 
angles are easy to handle in trigonometry; we can find their sines 
and cosines in a simple form, using only basic geometry. Here's are 
two of several pages in the Dr. Math archives that explain this:

   30-60-90 and 45-45-90 Triangles
   http://mathforum.org/dr.math/problems/kristina3.15.99.html   

   Deriving Sines of 30, 45, 60 and 90 Degrees
   http://mathforum.org/dr.math/problems/michael.6.02.99.html   

Another reason to work with these angles is that they arise 
frequently. The 30- and 60-degree angles are in equilateral triangles, 
and the 45- and 90-degree angles are in right isosceles triangles.

Yet another reason to use them is that they happen to be almost evenly 
spaced. If you included 15 and 75 degrees, they would be every 15 
degrees. I'll leave it to you to find the trig functions of 15 and 75 
degrees, and decide whether you would like to include them as standard 
angles as well.

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

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