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Chapter 6: Q 126 (page 397)

Show that the period off(胃)=csc胃is2蟺.

Short Answer

Expert verified

From the following graph of cosecant function f(胃)=csc胃it is clear that the period of cosecant function is 2蟺.

Step by step solution

01

Step 1. Given Information 

We have to prove that the period of cosecant function is 2蟺.

We will draw the graph of this function. After that from the graph we will examine the period of the function.

02

Step 2. To find period of cosecant function   

The given function is :-

f(胃)=csc胃

By using graphing utilities, we have the following graph of this function :-

We can see that curve of the graph repeated itself.

We know that the period of a function is where from the graph of function repeated itself.

We can see that the graph from 蟺2to 5蟺2is same as 5蟺2 to 9蟺2 and -3蟺2to 蟺2.

So we can conclude that the period of this function is :-

5蟺2-蟺2=2蟺.

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