Call Now to Set Up Tutoring:

(888) 888-0446

Trigonometry : Graphs of Inverse Trigonometric Functions

Study concepts, example questions & explanations for Trigonometry

Create An Account

All Trigonometry Resources

6 Diagnostic Tests 155 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Graphs Of Inverse Trigonometric Functions

True or False: The inverse of the function $\sin (x)$ is also a function.

Possible Answers:

True

False

Correct answer:

False

Explanation:

Consider the graph of the function sin(x) . It passes the vertical line test, that is if a vertical line is drawn anywhere on the graph it only passes through a single point of the function. This means that sin(x) is a function.

Screen shot 2020 08 27 at 11.59.46 am

Now, for its inverse to also be a function it must pass the horizontal line test. This means that if a horizontal line is drawn anywhere on the graph it will only pass through one point.

Screen shot 2020 08 27 at 12.00.18 pm

This is not true, and we can also see that if we graph the inverse of sin(x) ( $sin^{-1}(x)$ ) that this does not pass the vertical line test and therefore is not a function. If you wish to graph the inverse of sin(x) , then you must restrict the domain so that your graph will pass the vertical line test.

Screen shot 2020 08 27 at 12.00.40 pm

Report an Error

Example Question #2 : Graphs Of Inverse Trigonometric Functions

Which of the following is the graph of the inverse of sin(x) with $D: \frac{-\pi}{2} \leq x \leq \frac{\pi}{2}$ ?

Possible Answers:

Screen shot 2020 08 27 at 10.45.10 am

Screen shot 2020 08 27 at 10.47.13 am

Screen shot 2020 08 27 at 10.47.06 am

Screen shot 2020 08 27 at 10.46.15 am

Correct answer:

Screen shot 2020 08 27 at 10.46.15 am

Explanation:

Note that the inverse of sin(x) is not $\frac{1}{sin(x)}$ , that is the reciprocal. The inverse of sin(x) is $sin^{-1}(x)$ also written as arcsin(x) . The graph of sin(x) with $D: \frac{-\pi}{2} \leq x \leq \frac{\pi}{2}$ is as follows.

Screen shot 2020 08 27 at 10.45.10 am

And so the inverse of this graph must be the following with $D: -1 \leq x \leq 1$ and $R: \frac{-\pi}{2} \leq y \leq \frac{\pi}{2}$

Screen shot 2020 08 27 at 10.46.15 am

Report an Error

Example Question #3 : Graphs Of Inverse Trigonometric Functions

Which best describes the easiest method to graph an inverse trigonometric function (or any function) based on the parent function?

Possible Answers:

Let $x = \frac{1}{x}$ so where y = cos(x) for the parent function, $y = cos(\frac{1}{x})$ for the inverse function.

Let $y = \frac{1}{y}$ so where y = cos(x) for the parent function $y = \frac{1}{cos(x)}$ for the inverse function.

The and values are switched so where y = cos(x) for the parent function, x = cos(y) for the inverse function.

The values are swapped with $\frac{1}{y}$ so where y = cos(x) for the parent function, $x = cos(\frac{1}{y})$ for the inverse function.

Correct answer:

The and values are switched so where y = cos(x) for the parent function, x = cos(y) for the inverse function.

Explanation:

To find an inverse function you swap the and values. Take cos(x) for example, to find the inverse we use the following method.

y = cos(x)

x = cos(y) (swap the and values)

$cos^{-1}(x) = y$ (solving for )

$y = cos^{-1}(x)$

Report an Error

Example Question #4 : Graphs Of Inverse Trigonometric Functions

Which of the following represents the graph of $tan^{-1}(x)$ with $R: \frac{-\pi}{2} \leq y \leq \frac{\pi}{2}$ ?

Possible Answers:

Screen shot 2020 08 28 at 9.02.37 am

Screen shot 2020 08 28 at 9.00.48 am

Screen shot 2020 08 28 at 9.01.00 am

Screen shot 2020 08 28 at 9.02.30 am

Correct answer:

Screen shot 2020 08 28 at 9.01.00 am

Explanation:

If we are looking for the graph of $tan^{-1}(x)$ with $R: \frac{-\pi}{2} \leq x \leq \frac{\pi}{2}$ , that means this is the inverse of tan(x) with $D:\frac{-\pi}{2} \leq x \leq \frac{\pi}{2}$ . The graph of tan(x) with $D:\frac{-\pi}{2} \leq x \leq \frac{\pi}{2}$ is

Screen shot 2020 08 28 at 9.00.48 am

Switching the and values to graph the inverse we get the graph

Screen shot 2020 08 28 at 9.01.00 am

Report an Error

Example Question #5 : Graphs Of Inverse Trigonometric Functions

Which of the following is the graph of $cos^{-1}(x) + 2$ with $D: -1 \leq x \leq 1$ ?

Possible Answers:

Screen shot 2020 08 27 at 2.13.29 pm

Screen shot 2020 08 27 at 2.14.48 pm

Screen shot 2020 08 27 at 2.14.55 pm

Screen shot 2020 08 27 at 2.14.41 pm

Correct answer:

Screen shot 2020 08 27 at 2.13.29 pm

Explanation:

We first need to think about the graph of the function $cos^{-1}(x)$ .

Screen shot 2020 08 27 at 2.13.25 pm

Using the formula y = D + Acos(B(x - C)) where is the vertical shift, we have to perform a transformation of moving the function $cos^{-1}(x)$ up two units on the graph.

Screen shot 2020 08 27 at 2.13.29 pm

Report an Error

Example Question #6 : Graphs Of Inverse Trigonometric Functions

Which of the following is the correct graph and range of the inverse function of 2sin(x) with $D:\frac{-\pi}{2} \leq x \leq \frac{\pi}{2}$ ?

Possible Answers:

$R: \frac{-\pi}{2} \leq y \leq \frac{\pi}{2}$

Screen shot 2020 08 27 at 3.51.52 pm

$R:-\pi \leq y \leq \pi$

Screen shot 2020 08 27 at 3.51.52 pm

$R: \frac{-\pi}{2} \leq y \leq \frac{\pi}{2}$

Screen shot 2020 08 27 at 3.51.45 pm

$R:-\pi \leq y \leq \pi$

Screen shot 2020 08 27 at 3.51.45 pm

Correct answer:

$R: \frac{-\pi}{2} \leq y \leq \frac{\pi}{2}$

Screen shot 2020 08 27 at 3.51.52 pm

Explanation:

First, we must solve for the inverse of 2sin(x)

y = 2sin(x)

x = 2sin(y)

$\frac{x}{2} = sin(y)$

$sin^-1(\frac{x}{2}) = y$

So now we are trying to find the range of and plot the function $y = sin^{-1}(\frac{x}{2})$ . Let’s start with the graph of $sin^{-1}(x)$ . We know the domain is [-1,1] .

Screen shot 2020 08 27 at 3.51.45 pm

Now using the formula $y = D + Acos^{-1}(B(x-C))$ where $\frac{2\pi}{B}$ = Period, the period of $y = sin^{-1}(\frac{x}{2})$ is $4\pi$ . And so we perform a transformation to the graph of $sin^{-1}(x)$ to change the period from $2\pi$ to $4\pi$ .

Screen shot 2020 08 27 at 3.51.52 pm

We can see that the graph has a range of $[\frac{-\pi}{2},\frac{\pi}{2}]$

Report an Error

Example Question #7 : Graphs Of Inverse Trigonometric Functions

True or False: The domain for arctan(x) will always be all real numbers no matter the value of or any transformations applied to the tangent function.

Possible Answers:

False

True

Correct answer:

True

Explanation:

This is true because just as the range of tan(x) is all real numbers due to the vertical asymptotes of the function, the function arctan(x) extends to all values of but is limited in its values of . No matter the transformations applied, all values of will still be reached.

Report an Error

Example Question #8 : Graphs Of Inverse Trigonometric Functions

Which of the following is the graph of $\frac{1}{2}cos^{-1}(x) + 1$ ?

Possible Answers:

Screen shot 2020 08 27 at 1.57.17 pm

Screen shot 2020 08 27 at 1.55.06 pm

Screen shot 2020 08 27 at 1.54.54 pm

Screen shot 2020 08 27 at 1.55.00 pm

Correct answer:

Screen shot 2020 08 27 at 1.55.06 pm

Explanation:

First, we must consider the graph of $cos^{-1}(x)$ .

Screen shot 2020 08 27 at 1.54.54 pm

Using the formula $D + Acos^{-1}(B(x-C))$ we can apply the transformations step-by-step. First we will transform the amplitude, so $A = \frac{1}{2}$ so we must shorten the amplitude to $\frac{1}{2}$ .

Screen shot 2020 08 27 at 1.55.00 pm

Now we must apply a vertical shift of one unit since D=1 . This leaves us with our answer.

Screen shot 2020 08 27 at 1.55.06 pm

Report an Error

View Trigonometry Tutors

Jody
Certified Tutor

The University of Texas at Austin, Bachelor of Science, Mathematics.

View Trigonometry Tutors

Omar
Certified Tutor

Arizona State University, Bachelors, Civil Engineering.

View Trigonometry Tutors

James
Certified Tutor

Purdue University-Main Campus, Doctor of Education, Mathematics Teacher Education.

All Trigonometry Resources

6 Diagnostic Tests 155 Practice Tests Question of the Day Flashcards Learn by Concept

Trigonometry Tutors in Top Cities:

Popular Courses & Classes

ISEE Courses & Classes in Washington DC, GMAT Courses & Classes in Chicago, MCAT Courses & Classes in Atlanta, GMAT Courses & Classes in Denver, SSAT Courses & Classes in San Diego, GMAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Chicago, SSAT Courses & Classes in Chicago, SAT Courses & Classes in New York City

Popular Test Prep

MCAT Test Prep in Chicago, SAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Dallas Fort Worth, SAT Test Prep in Houston, MCAT Test Prep in Miami, MCAT Test Prep in Atlanta, SAT Test Prep in Philadelphia, GMAT Test Prep in Philadelphia, GRE Test Prep in Boston, LSAT Test Prep in Washington DC

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Trigonometry : Graphs of Inverse Trigonometric Functions

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #1 : Graphs Of Inverse Trigonometric Functions

Example Question #2 : Graphs Of Inverse Trigonometric Functions

Example Question #3 : Graphs Of Inverse Trigonometric Functions

Example Question #4 : Graphs Of Inverse Trigonometric Functions

Example Question #5 : Graphs Of Inverse Trigonometric Functions

Example Question #6 : Graphs Of Inverse Trigonometric Functions

Example Question #7 : Graphs Of Inverse Trigonometric Functions

Example Question #8 : Graphs Of Inverse Trigonometric Functions

All Trigonometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: