Small-angle approximation: Difference between revisions

Revision as of 19:11, 6 December 2007

Revision as of 12:40, 15 March 2008

Line 23:

:<math>\tan\left( x \right) = x + \frac{x^3}{3} + \frac{2 x^5}{15} + \frac{17 x^7}{315} + \cdots</math>

When the angle ''x'' is less than one radian, its powers ''x''², ''x''³, ... [[exponential decay|decrease exponentially]]rapidly, so only a few are needed. The highest power included is called the order of the approximation. Neither sin(''x'') nor tan(''x'') has an ''x''² term, so their first- and second-order approximations are the same.

== Specific uses ==