Call Now to Set Up Tutoring:

(888) 888-0446

Create an account to track your scores
and create your own practice tests:

Create an Account Create a Practice Test

All Common Core: High School - Functions Resources

6 Diagnostic Tests 82 Practice Tests Question of the Day Flashcards Learn by Concept

Want to review Common Core: High School - Functions but don’t feel like sitting for a whole test at the moment? Varsity Tutors has you covered with thousands of different Common Core: High School - Functions flashcards! Our Common Core: High School - Functions flashcards allow you to practice with as few or as many questions as you like. Get some studying in now with our numerous Common Core: High School - Functions flashcards.

Flashcards: Restricting Domain of Trigonometric Functions to Allow for Construction of Inverse: CCSS.Math.Content.HSF-TF.B.6

Find the exact value of the following statement.

$f(x)=\cos^{-1}(1)$

$2\pi$

$-\pi$

$\pi$

$\frac{\pi}{3}$

$\frac{\pi}{2}$

Report an Error Copyright Notice

Flashcards: Restricting Domain of Trigonometric Functions to Allow for Construction of Inverse: CCSS.Math.Content.HSF-TF.B.6

Find the exact value of the following statement.

$f(x)=\cos^{-1}(1)$

Your answer:

$-\pi$

Your answer:

$\pi$

Your answer:

$\frac{\pi}{3}$

Your answer:

$\frac{\pi}{2}$

Correct answer:

$2\pi$

Explanation:

This question is testing ones ability to understand and identify inverses of trigonometric functions as they relate to the unit circle.

For the purpose of Common Core Standards, " Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed." concept (CCSS.MATH.CONTENT.HSF-TF.B.6). It is important to note that this standard is not directly tested on but is used for building a deeper understanding on trigonometric functions.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Since there is a trigonometric function raised to the negative one power, this question is talking about the inverse of the function. In other words, which angle on the unit circle results in a cosine equalling one?

$y=\cos^{-1}(a)\Rightarrow \cos(\theta)=a$

Therefore, theta needs to be solved for.

Step 2: Draw and label the unit circle.

Screen shot 2016 01 14 at 10.52.42 am

Step 3: Locate the angle that results in one for its cosine value.

Recall that

$(x,y)=(\cos(\theta),\sin(\theta))$

therefore look for the (x,y) that has x=1 . Looking at the unit circle from step 2, it is seen that at angle $2\pi$ the cosine equals one.

Thus,

$f(x)=\cos^{-1}(1)\Rightarrow f(x)=2\pi$

To verify the solution simply find the cosine of the angle theta.

$\cos(2\pi)=1\rightarrow\cos^{-1}(1)=2\pi$

Flashcards: Restricting Domain of Trigonometric Functions to Allow for Construction of Inverse: CCSS.Math.Content.HSF-TF.B.6

Find the exact value of the following statement.

$f(x)=\sin^{-1}(-1)$

$\sin^{-1}(-1)=\pi$

$\sin^{-1}(-1)=\frac{3\pi}{4}$

$\sin^{-1}(-1)=2\pi$

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

$\sin^{-1}(-1)=\frac{3\pi}{2}$

Report an Error Copyright Notice

Flashcards: Restricting Domain of Trigonometric Functions to Allow for Construction of Inverse: CCSS.Math.Content.HSF-TF.B.6

Find the exact value of the following statement.

$f(x)=\sin^{-1}(-1)$

Your answer:

$\sin^{-1}(-1)=\pi$

Your answer:

$\sin^{-1}(-1)=\frac{3\pi}{4}$

Your answer:

$\sin^{-1}(-1)=2\pi$

Your answer:

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

Correct answer:

$\sin^{-1}(-1)=\frac{3\pi}{2}$

Explanation:

This question is testing ones ability to understand and identify inverses of trigonometric functions as they relate to the unit circle.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

$y=\sin^{-1}(a)\Rightarrow \sin(\theta)=a$

Therefore, theta needs to be solved for.

Step 2: Draw and label the unit circle.

Screen shot 2016 01 14 at 10.52.42 am

Step 3: Locate the angle that results in negative one for its sine value.

Recall that

$(x,y)=(\cos(\theta),\sin(\theta))$

therefore look for the (x,y) that has y=-1 . Looking at the unit circle from step 2, it is seen that at angle $\frac{3\pi}{2}$ the sine equals negative one.

Thus,

$f(x)=\sin^{-1}(-1)\Rightarrow f(x)=\frac{3\pi}{2}$

To verify the solution simply find the sine of the angle theta.

$\sin\left(\frac{3\pi}{2}\right)=-1\rightarrow\sin^{-1}(-1)=\frac{3\pi}{2}$

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)

View Tutors

Tejal
Certified Tutor

Ottawa University-Online, Bachelor of Fine Arts, Education. Ottawa University-Online, Masters in Education, Educational, Inst...

View Tutors

Marguerita
Certified Tutor

Mississippi College, Bachelor in Arts, Journalism. Mississippi College, Master of Arts Teaching, High School Teaching.

View Tutors

Oluwaferanmi
Certified Tutor

Indiana University-Bloomington, Bachelor of Science, Biotechnology.

Popular Subjects

Biology Tutors in Phoenix, French Tutors in Miami, Math Tutors in Boston, LSAT Tutors in Los Angeles, Calculus Tutors in San Diego, Physics Tutors in Dallas Fort Worth, SAT Tutors in Dallas Fort Worth, Reading Tutors in Boston, GMAT Tutors in Philadelphia, Physics Tutors in San Francisco-Bay Area

Popular Courses & Classes

SAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Seattle, LSAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Chicago, ACT Courses & Classes in Atlanta, LSAT Courses & Classes in San Diego, LSAT Courses & Classes in Washington DC, Spanish Courses & Classes in Philadelphia, SSAT Courses & Classes in Boston

Popular Test Prep

ACT Test Prep in Washington DC, MCAT Test Prep in Phoenix, MCAT Test Prep in San Diego, GRE Test Prep in Miami, GRE Test Prep in Washington DC, ACT Test Prep in Atlanta, SSAT Test Prep in Los Angeles, SSAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Miami, GRE Test Prep in San Diego

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Create an account to track your scores
and create your own practice tests:

All Common Core: High School - Functions Resources

Flashcards: Restricting Domain of Trigonometric Functions to Allow for Construction of Inverse: CCSS.Math.Content.HSF-TF.B.6

Flashcards: Restricting Domain of Trigonometric Functions to Allow for Construction of Inverse: CCSS.Math.Content.HSF-TF.B.6

Flashcards: Restricting Domain of Trigonometric Functions to Allow for Construction of Inverse: CCSS.Math.Content.HSF-TF.B.6

Flashcards: Restricting Domain of Trigonometric Functions to Allow for Construction of Inverse: CCSS.Math.Content.HSF-TF.B.6

Report an issue with this question