Limits of trigonometric functions

Evaluating trigonometric limits, examples

Evaluating trigonometric limits examples

We use the fundamental limit and known trigonometric identities when solving trigonometric

limits.

Example:  Evaluate the limit

Solution:

Example:  Evaluate the limit

Solution:   Since  cos(a + b) = cosacosb - sinasinb   then   cos2a = cos2a - sin2a = 1 - 2sin2a

that is

Example:  Evaluate the limit

Solution:   We use the sum to product identity and the fundamental trigonometric limit, thus

Example:  Evaluate the limit

Solution:   If we substitute  arcsin (x + 2) = t   then,

x + 2 = sin t  or  x = sin t - 2  so that,   t ® 0  as x ® -2,  therefore

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