On-line Math 21

3.1  Trigonometric functions

3.1.2  Limits of trig functions

In order to understand the calculus of sin(x) , or any trigonometric function, we first need to find some limits involving trigonometric functions. First, we deal with the limit

lim x® 0  sin(x) x = 1.

Derivation

All other trigonometric limits we will need follow from this one. Here are some examples.

Example 1

lim x® 0  cos(x)-1 x = 0

Solution

Exercise 1

lim x® 0  tan(x) x =

Exercise 2

lim x® 0  sin(3x) sin(4x) =

Hint

Exercise 3

lim x® 0  cos(x)-1 x2 =

Email Address (Required to submit answers):