Small angle approximation

The Small angle approximation is a rule that says that for small angles, the trigonometric functions sine and tangent are approximately equal to the angle. This approximation is relevant only when angles are measured in radians. Of course, the equality is not exact; only when the angle is zero are the three truly equal. In symbolic terms:

$\theta \approx \sin \theta \approx \tan \theta$

Using the rule, a physical equation such as the equation for diffraction minima:

$b\sin(\theta )=m\lambda$

might become

$b\theta =m\lambda$.

The equation can then be written as a pure product of quantities with whole-numbered exponents, which is sometimes useful.

The rule is very useful to an engineer performing experiments or making approximations. It is probably best to avoid it when accuracy is important, or when larger angles are expected.