Trigonometric Limits

Solved Problems

Solution.

Obviously, $$ and $$ as $$ Then

Solution.

Using the identity

convert the limit:

Change the variable: $$ When $$ then $$ or $$ Hence,

Solution.

We apply the following transformations:

As $$ we have

Here

Hence,

Here $$ as $$ Therefore

Solution.

We make the substitution: $$ When $$ then $$ As a result, we have

Solution.

We use the trigonometric formula:

Then the limit can be written in the form