Standard AnglesDate: 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/ |
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