exact trigonometry tables
0.1 Basic angles
Since the trigonometric ratios for most angles cannot be calculated exactly in closed algebraic form, a few well-known angles that can be calculated often comprise the bulk of textbook exercises involving trigonometry.
The basic angles are given in Table 1.
0.2 Other angles by addition and halving
These basic angles can be easily extended to obtain more angles of interest. Adding multiples of merely rotates these angles into other quadrants; the appropriate values of and can be obtained through symmetry.
The values for can be obtained by using the formula for the difference of angles (http://planetmath.org/AngleSumIdentity):
Likewise, we can find that
More exact angles can be obtained by solving the double angle identity:
So for example, . These angles can be further added and subdivided to obtain a dense subset of exactly known angles. However, such effort is not generally useful. Computers and calculators use a combination of lookup-tables and numeric iteration to obtain their values.
0.3 The angles , , ,
The --- series of angles cannot be obtained by halving, doubling, adding or subtracting the previous angles. Nevertheless, they are constructible, and their exact values can be derived by the following elementary procedure:
Notice that and , so if , then
|Title||exact trigonometry tables|
|Date of creation||2013-03-22 15:31:26|
|Last modified on||2013-03-22 15:31:26|
|Last modified by||stevecheng (10074)|