Associated Topics || Dr. Math Home || Search Dr. Math

### 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

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