Small-angle approximation

Small angle approximation is a way of estimating angles in radians, where the angle is small (less than 3 or 4 degrees).

When x is small, and in radians, the following formulae are true:

${\displaystyle \sin x\simeq x}$

${\displaystyle \cos x\simeq 1-{\frac {x^{2}}{2}}}$

${\displaystyle \tan x\simeq x}$

The following key characteristic can be derived from the above for a right triangle with sides A, B, and H, where H is the hypothenuse and A is opposite angle x:

${\displaystyle \sin x=\tan x}$

${\displaystyle {\frac {A}{H}}={\frac {A}{Y}}}$

${\displaystyle H=Y}$