Small-angle approximation

Approximately equal behavior of some (trigonometric) functions for x → 0

The small-angle approximations can be used to approximate the values of the main trigonometric functions, provided that the angle in question is small and is measured in radians:

These approximations have a wide range of uses in branches of physics and engineering, including mechanics, electromagnetism, optics, cartography, astronomy, and computer science.[1][2] One reason for this is that they can greatly simplify differential equations that do not need to be answered with absolute precision.

There are a number of ways to demonstrate the validity of the small-angle approximations. The most direct method is to truncate the Maclaurin series for each of the trigonometric functions. Depending on the order of the approximation, is approximated as either or as .[3]

  1. ^ Cite error: The named reference Holbrow2010 was invoked but never defined (see the help page).
  2. ^ Cite error: The named reference Plesha2012 was invoked but never defined (see the help page).
  3. ^ "Small-Angle Approximation | Brilliant Math & Science Wiki". brilliant.org. Retrieved 2020-07-22.