Chapter 6: Q 124 (page 397)

Show that the period of $f (θ) = \cos θ$ is $2 π$ .

Short Answer

Expert verified

From the following graph of cosine function $f (θ) = \cos θ$ it is clear that the period of cosine function is $2 π$ .

Step by step solution

Step 1. Given Information

We have to prove that the period of cosine function is $2 π$ .

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

Step 2. To find period of cosine function

The given function is :-

$f (θ) = \cos θ$ .

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 after $2 π$ , repeating itself as it is from $0$ to $2 π$ .

Similarly the graph is from $- 2 π$ to $0$ is same as $0$ to $2 π$ .

So we can conclude that the period of the given function is $2 π$ .

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Show that the period of $f (θ) = \cos θ$ is $2 π$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. To find period of cosine function

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Show that the period off(θ)=cosθis2π.

Short Answer

Step by step solution

Step 1. Given Information

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Show that the period of $f (θ) = \cos θ$ is $2 π$ .