Chapter 6: Q 126 (page 397)

Show that the period of $f (θ) = c s c θ$ is $2 π$ .

Short Answer

Expert verified

From the following graph of cosecant function $f (θ) = c s c θ$ it is clear that the period of cosecant function is $2 π$ .

Step by step solution

Step 1. Given Information

We have to prove that the period of cosecant 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 cosecant function

The given function is :-

$f (θ) = c s c θ$

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 the graph from $\frac{π}{2}$ to $\frac{5 π}{2}$ is same as $\frac{5 π}{2}$ to $\frac{9 π}{2}$ and $\frac{- 3 π}{2}$ to $\frac{π}{2}$ .

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

$\frac{5 π}{2} - \frac{π}{2} = 2 π$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Show that the period of $f (θ) = c s c θ$ is $2 π$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. To find period of cosecant function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Theoretical and Mathematical Physics

Statistics

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Show that the period off(θ)=cscθis2π.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. To find period of cosecant function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Theoretical and Mathematical Physics

Statistics

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Show that the period of $f (θ) = c s c θ$ is $2 π$ .