Small Angle Approximation

Concept

For all small angle approximation, positive or negative, we have

(1)

(2)

(3) approximating the small angle for cosine, is measured in radians

Small angle approximation can be applied only when a small angle is defined as such :

In the following situations when k=1,2,3:

(a) b) small angle approxiation k for tangentc)

Scholar's Tip : In applying the above formulas, we have to ensure that the value of is small enough so that the approximation of the angle is valid.

Examples

Make use of the concept of small angle approximation for the following examples.

a)Find an expression for

It's important to use the approximate sign when we are approaching the approximating small angles

b) Find an expression for if is small enough to neglect and above.

small angle approximation for the cosine function

=

It is possible to further simplify this expression using binominal series.

So

=

solution for small angle approximation

We ignore and above since they tend towards zero. This is because is small.

Look at the law of sines and law of cosines .

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