What is small angle approximation?

The small angle approximation is a mathematical technique used to simplify trigonometric calculations when dealing with angles that are very close to zero.

When the angle θ is very small, it is common to approximate trigonometric functions such as sine, cosine, and tangent using simple linear approximations. In this case, the sine of a small angle can be approximated as the angle itself, the cosine of a small angle can be approximated as 1, and the tangent of a small angle can be approximated as the angle itself.

The small angle approximation is particularly useful in physics and engineering when dealing with situations where small angles are encountered, such as in pendulum motion, sound waves, optics, and vibrations. By making use of the small angle approximation, complex trigonometric calculations can be simplified and approximated with a high degree of accuracy.