Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : How to find the domain of the tangent

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find The Domain Of The Tangent

What is domain of the function $\tan(\theta)$ from the interval $[-\pi,\pi]$ ?

Possible Answers:

$\left[-\pi, \frac{-\pi}{2}\right]\cup \left[\frac{\pi}{2},\pi\right]$

$\left(-\pi, \frac{-\pi}{2}\right)\cup \left(\frac{\pi}{2},\pi\right)$

$\left[-\pi, \frac{-\pi}{2}\right)\cup \left(\frac{-\pi}{2},\frac{\pi}{2}\right) \cup \left(\frac{\pi}{2},\pi\right]$

$\left[-\pi, \frac{-\pi}{2}\right)\cup \left(\frac{\pi}{2},\pi\right]$

$\left[-\pi, \frac{-\pi}{2}\right]\cup\left[\frac{-\pi}{2},\frac{\pi}{2}\right] \cup\left[\frac{\pi}{2},\pi\right]$

Correct answer:

$\left[-\pi, \frac{-\pi}{2}\right)\cup \left(\frac{-\pi}{2},\frac{\pi}{2}\right) \cup \left(\frac{\pi}{2},\pi\right]$

Explanation:

Rewrite the tangent function in terms of cosine and sine.

$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$

Since the denominator cannot be zero, evaluate all values of theta where $\cos(\theta)=0$ on the interval $[-\pi,\pi]$ .

$\theta=-\frac{\pi}{2}, \frac{\pi}{2}$

These values of theta are asymptotes and will not exist on the tangent curve. They will not be included in the domain and parentheses will be used in the interval notation.

The correct solution is $\left[-\pi, \frac{-\pi}{2}\right)\cup \left(\frac{-\pi}{2},\frac{\pi}{2}\right) \cup \left(\frac{\pi}{2},\pi\right]$ .

Report an Error

Example Question #2 : How To Find The Domain Of The Tangent

Where does the domain NOT exist for $y=2tan(x-\frac{\pi}{2})+3$ ?

Possible Answers:

$x=2\pi+\frac{\pi}{2} k \textup{, for k any integer}$

$x=\pi+\pi k \textup{, for k any integer}$

$x=\pi+2\pi k \textup{, for k any integer}$

$x=3\pi+\frac{\pi}{2} k \textup{, for k any integer}$

$x=2\pi+2\pi k \textup{, for k any integer}$

Correct answer:

$x=\pi+\pi k \textup{, for k any integer}$

Explanation:

The domain for the parent function of tangent does not exist for:

$x=\frac{\pi}{2}+\pi k \textup{, for k any integer.}$

The amplitude and the vertical shift will not affect the domain or the period of the graph.

The $x-\frac{\pi}{2}$ tells us that the graph will shift right $\frac{\pi}{2}$ units.

Therefore, the asymptotes will be located at:

$x=\frac{\pi}{2}+\pi k+ \frac{\pi}{2} \textup{, for k any integer.}$

The locations of the asymptotes are:

$x=\pi+\pi k \textup{, for k any integer}$

Report an Error

Example Question #3 : How To Find The Domain Of The Tangent

Find the domain of $y=tan(x-\frac{3\pi}{4})$ . Assume is for all real numbers.

Possible Answers:

$\textup{Everywhere except: }x=\frac{3\pi}{4}\pm \pi k$

$x=\frac{5\pi}{4}\pm \pi k$

$\textup{Everywhere except: }x=\frac{5\pi}{4}\pm \frac{\pi}{2} k$

$x=\frac{3\pi}{4}\pm \pi k$

$\textup{Everywhere except: }x=\frac{5\pi}{4}\pm \pi k$

Correct answer:

$\textup{Everywhere except: }x=\frac{5\pi}{4}\pm \pi k$

Explanation:

The domain of tan(x) does not exist at $\frac{\pi}{2}\pm \pi k$ , for is an integer.

The ends of every period approaches to either positive or negative infinity. Notice that for this problem, the entire graph shifts to the right $\frac{3\pi}{4}$ units. This means that the asymptotes would also shift right by the same distance.

The asymptotes will exist at:

$x=\frac{\pi}{2}\pm \pi k + \frac{3\pi}{4} = \frac{5\pi}{4}\pm \pi k$

Therefore, the domain of $y=tan(x-\frac{3\pi}{4})$ will exist anywhere EXCEPT:

$\frac{5\pi}{4}\pm \pi k$

Report an Error

View ACT Math Tutors

Odesha
Certified Tutor

Alabama State University, Bachelors, Chemistry.

View ACT Math Tutors

Bibhash
Certified Tutor

Pune University, Bachelor in Arts, Ecommerce. SDA Bocconi School of Management, Masters in Business Administration, Finance.

View ACT Math Tutors

Rachel
Certified Tutor

University of Arkansas at Little Rock, Bachelor in Arts, Mathematics.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

GRE Courses & Classes in Phoenix, Spanish Courses & Classes in San Diego, ISEE Courses & Classes in Seattle, GRE Courses & Classes in Los Angeles, MCAT Courses & Classes in Denver, LSAT Courses & Classes in Seattle, Spanish Courses & Classes in Chicago, LSAT Courses & Classes in Atlanta, Spanish Courses & Classes in Los Angeles, SAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

ISEE Test Prep in Chicago, SAT Test Prep in Philadelphia, GMAT Test Prep in Atlanta, SAT Test Prep in Washington DC, ISEE Test Prep in Atlanta, MCAT Test Prep in Washington DC, GRE Test Prep in Los Angeles, MCAT Test Prep in Denver, ACT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Philadelphia

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

ACT Math : How to find the domain of the tangent

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Find The Domain Of The Tangent

Example Question #2 : How To Find The Domain Of The Tangent

Example Question #3 : How To Find The Domain Of The Tangent

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: