Limits on Trigonometric Functions

Limits on Trigonometric Functions

The limits of trigonometric functions play a fundamental role in calculus, particularly in defining derivatives. One of the most important results is:

A fundamental trigonometric limit is the limit of sine theta divided by theta as theta approaches zero, which equals one.

To visualize, consider a unit circle and a small angle theta measured from the positive x-axis.

An arc corresponding to this angle is drawn. For a unit circle, the arc length is numerically equal to the angle in r...