# Understanding the limit of trig functions:

We already know that limit is defined by the value a function attains when the index number approaches a particular point. In the similar fashion, **limits of trigonometric function** can be known by the value they attain when its input index reaches the given value. The **limits of trig functions** can also be obtained from the graphs of this functions.

The examples given below will help to understand the **limit of trig functions**.

(1) Find the limit for

Here we need to calculate the limit when index x approaches 0. Hence putting x = 0 in above trigonometric function, we know that cos 0 = 1 and sin 0 = 0. Thus limit L = 1 / (0 – 3) = -1/3. Thus the limit of above function for x -> 0 is -1/3.

(2) Evaluate

Since x -> 0+, value of cot x has to be in first quadrant i.e. positive values. Now cot x = cos x / sin x. Hence cot 0 = cos 0 / sin 0 = 1 / 0 = ∞. Hence there is need to compute the denominator. The limit of this function is a positive infinity. Thus this function will be having a vertical asymptote at x = 0.

(3) Evaluate

If we directly find the limit of above function, it comes to 0 / 0 = ∞. But we have a formula for limit which says that limit of a function f of x divided by x is 1, i.e .Here f(x) = sin x. Thus using this formula, we get the limit of this function as 1.

Thus we have understood the theory for finding **limits of trigonometric functions **and solved some examples related to it. This limit properties can be used as a basis for derivatives, integration and for other applications.

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