Call Now to Set Up Tutoring:

(888) 888-0446

Common Core: High School - Functions : Trigonometric Functions

Study concepts, example questions & explanations for Common Core: High School - Functions

Create An Account

All Common Core: High School - Functions Resources

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

Example Questions

← Previous 1 2 3 4 5 6 7 8 9 10 11 Next →

Example Question #5 : Symmetry And Periodicity Of Trigonometric Functions: Ccss.Math.Content.Hsf.Tf.B.4

Find the following trigonometric exact value.

$\cos\left(\frac{7\pi}{6} \right )$

Possible Answers:

$\cos\left(\frac{7\pi}{6} \right )=-\frac{\sqrt{3}}{2}$

$\cos\left(\frac{7\pi}{6} \right )=-\frac{1}{2}$

$\cos\left(\frac{7\pi}{6} \right )=\frac{\sqrt{3}}{2}$

$\cos\left(\frac{7\pi}{6} \right )=-\frac{\sqrt{2}}{2}$

$\cos\left(\frac{7\pi}{6} \right )=\frac{1}{2}$

Correct answer:

$\cos\left(\frac{7\pi}{6} \right )=-\frac{\sqrt{3}}{2}$

Explanation:

This question tests one's ability to recognize and use the unit circle to calculate the exact trigonometric value.

For the purpose of Common Core Standards, "Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions." falls within the Cluster A of "Extend the domain of trigonometric functions using the unit circle" concept (CCSS.MATH.CONTENT.HSF-TF.A.4).

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: Recall the unit circle.

Screen shot 2016 01 14 at 10.52.42 am

Step 2: Identify the (x,y) coordinate pair that represents the extension of $\theta = \frac{7\pi}{6}$ .

$\theta = \frac{7\pi}{6}\Rightarrow \left(-\frac{\sqrt{3}}{2}, -\frac{1}{2} \right )$

Step 3: Calculate the exact value of $\cos\left(\frac{7\pi}{6} \right )$ .

Recall that,

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

therefore,

$\left(-\frac{\sqrt{3}}{2},-\frac{1}{2}\right)=\left(\cos\left(\frac{7\pi}{6}\right),\sin\left(\frac{7\pi}{6}\right)\right)$

$\cos\left(\frac{7\pi}{6} \right )=-\frac{\sqrt{3}}{2}$ .

Report an Error

Example Question #6 : Symmetry And Periodicity Of Trigonometric Functions: Ccss.Math.Content.Hsf.Tf.B.4

Find the following trigonometric exact value.

$\sin\left(\frac{7\pi}{6} \right )$

Possible Answers:

$\sin\left(\frac{7\pi}{6} \right )=-\frac{1}{2}$

$\sin\left(\frac{7\pi}{6} \right )=\frac{1}{\sqrt{2}}$

$\sin\left(\frac{7\pi}{6} \right )=\frac{1}{2}$

$\sin\left(\frac{7\pi}{6} \right )=-\frac{1}{\sqrt{2}}$

$\sin\left(\frac{7\pi}{6} \right )=-\frac{\sqrt{3}}{2}$

Correct answer:

$\sin\left(\frac{7\pi}{6} \right )=-\frac{1}{2}$

Explanation:

This question tests one's ability to recognize and use the unit circle to calculate the exact trigonometric value.

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: Recall the unit circle.

Screen shot 2016 01 14 at 10.52.42 am

Step 2: Identify the (x,y) coordinate pair that represents the extension of $\theta = \frac{7\pi}{6}$ .

$\theta = \frac{7\pi}{6}\Rightarrow \left(-\frac{\sqrt{3}}{2}, -\frac{1}{2} \right )$

Step 3: Calculate the exact value of $\sin\left(\frac{7\pi}{6} \right )$ .

Recall that,

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

therefore,

$\left(-\frac{\sqrt{3}}{2},-\frac{1}{2}\right)=\left(\cos\left(\frac{7\pi}{6}\right),\sin\left(\frac{7\pi}{6}\right)\right)$

$\sin\left(\frac{7\pi}{6} \right )=-\frac{1}{2}$ .

Report an Error

Example Question #7 : Symmetry And Periodicity Of Trigonometric Functions: Ccss.Math.Content.Hsf.Tf.B.4

Find the following trigonometric exact value.

$\cos\left(\frac{11\pi}{6} \right )$

Possible Answers:

$\cos\left(\frac{11\pi}{6} \right )=-\frac{\sqrt{3}}{2}$

$\cos\left(\frac{11\pi}{6} \right )=-\frac{1}{2}$

$\cos\left(\frac{11\pi}{6} \right )=\frac{\sqrt{3}}{2}$

$\cos\left(\frac{11\pi}{6} \right )={\sqrt{3}}$

$\cos\left(\frac{11\pi}{6} \right )=\frac{1}{2}$

Correct answer:

$\cos\left(\frac{11\pi}{6} \right )=\frac{\sqrt{3}}{2}$

Explanation:

This question tests one's ability to recognize and use the unit circle to calculate the exact trigonometric value.

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: Recall the unit circle.

Screen shot 2016 01 14 at 10.52.42 am

Step 2: Identify the (x,y) coordinate pair that represents the extension of $\theta = \frac{11\pi}{6}$ .

$\theta = \frac{11\pi}{6}\Rightarrow \left(\frac{\sqrt{3}}{2}, -\frac{1}{2} \right )$

Step 3: Calculate the exact value of $\cos\left(\frac{11\pi}{6} \right )$ .

Recall that,

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

therefore,

$\left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right)=\left(\cos\left(\frac{11\pi}{6}\right),\sin\left(\frac{11\pi}{6}\right)\right)$

$\cos\left(\frac{11\pi}{6} \right )=\frac{\sqrt{3}}{2}$ .

Report an Error

Example Question #8 : Symmetry And Periodicity Of Trigonometric Functions: Ccss.Math.Content.Hsf.Tf.B.4

Find the following trigonometric exact value.

$\sin\left(\frac{11\pi}{6} \right )$

Possible Answers:

$\sin\left(\frac{11\pi}{6} \right )=\frac{\sqrt{3}}{2}$

$\sin\left(\frac{11\pi}{6} \right )=-\frac{1}{\sqrt{2}}$

$\sin\left(\frac{11\pi}{6} \right )=-\frac{1}{2}$

$\sin\left(\frac{11\pi}{6} \right )=\frac{1}{2}$

$\sin\left(\frac{11\pi}{6} \right )=-\frac{\sqrt{3}}{2}$

Correct answer:

$\sin\left(\frac{11\pi}{6} \right )=-\frac{1}{2}$

Explanation:

This question tests one's ability to recognize and use the unit circle to calculate the exact trigonometric value.

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: Recall the unit circle.

Screen shot 2016 01 14 at 10.52.42 am

Step 2: Identify the (x,y) coordinate pair that represents the extension of $\theta = \frac{11\pi}{6}$ .

$\theta = \frac{11\pi}{6}\Rightarrow \left(\frac{\sqrt{3}}{2}, -\frac{1}{2} \right )$

Step 3: Calculate the exact value of $\sin\left(\frac{11\pi}{6} \right )$ .

Recall that,

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

therefore,

$\left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right)=\left(\cos\left(\frac{11\pi}{6}\right),\sin\left(\frac{11\pi}{6}\right)\right)$

$\sin\left(\frac{11\pi}{6} \right )=-\frac{1}{2}$ .

Report an Error

Example Question #9 : Symmetry And Periodicity Of Trigonometric Functions: Ccss.Math.Content.Hsf.Tf.B.4

Find the following trigonometric exact value.

$\cos\left(\frac{\pi}{4} \right )$

Possible Answers:

$\cos\left(\frac{\pi}{4} \right )=\frac{1}{2}$

$\cos\left(\frac{\pi}{4} \right )=-\frac{1}{\sqrt{2}}$

$\cos\left(\frac{\pi}{4} \right )=-\frac{1}{2}$

$\cos\left(\frac{\pi}{4} \right )=\frac{1}{\sqrt{2}}$

$\cos\left(\frac{\pi}{4} \right )=\sqrt{2}$

Correct answer:

$\cos\left(\frac{\pi}{4} \right )=\frac{1}{\sqrt{2}}$

Explanation:

This question tests one's ability to recognize and use the unit circle to calculate the exact trigonometric value.

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: Recall the unit circle.

Screen shot 2016 01 14 at 10.52.42 am

Step 2: Identify the (x,y) coordinate pair that represents the extension of $\theta = \frac{\pi}{4}$ .

$\theta = \frac{\pi}{4}\Rightarrow \left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \right )$

Step 3: Calculate the exact value of $\cos\left(\frac{\pi}{4} \right )$ .

Recall that,

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

therefore,

$\left(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}\right)=\left(\cos\left(\frac{\pi}{4}\right),\sin\left(\frac{\pi}{4}\right)\right)$

$\cos\left(\frac{\pi}{4} \right )=\frac{1}{\sqrt{2}}$ .

Report an Error

Example Question #10 : Symmetry And Periodicity Of Trigonometric Functions: Ccss.Math.Content.Hsf.Tf.B.4

Find the following trigonometric exact value.

$\sin\left(\frac{\pi}{4} \right )$

Possible Answers:

$\sin\left(\frac{\pi}{4} \right )=-\frac{1}{\sqrt{2}}$

$\sin\left(\frac{\pi}{4} \right )=-\frac{1}{2}$

$\sin\left(\frac{\pi}{4} \right )=\frac{1}{2}$

$\sin\left(\frac{\pi}{4} \right )=\frac{1}{\sqrt{2}}$

$\sin\left(\frac{\pi}{4} \right )=-\sqrt{2}$

Correct answer:

$\sin\left(\frac{\pi}{4} \right )=\frac{1}{\sqrt{2}}$

Explanation:

This question tests one's ability to recognize and use the unit circle to calculate the exact trigonometric value.

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: Recall the unit circle.

Screen shot 2016 01 14 at 10.52.42 am

Step 2: Identify the (x,y) coordinate pair that represents the extension of $\theta = \frac{\pi}{4}$ .

$\theta = \frac{\pi}{4}\Rightarrow \left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \right )$

Step 3: Calculate the exact value of $\sin\left(\frac{\pi}{4} \right )$ .

Recall that,

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

therefore,

$\left(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}\right)=\left(\cos\left(\frac{\pi}{4}\right),\sin\left(\frac{\pi}{4}\right)\right)$

$\sin\left(\frac{\pi}{4} \right )=\frac{1}{\sqrt{2}}$ .

Report an Error

Example Question #41 : Trigonometric Functions

Find the following trigonometric exact value.

$\cos\left(\frac{3\pi}{4} \right )$

Possible Answers:

$\cos\left(\frac{3\pi}{4} \right )=-\frac{1}{2}$

$\cos\left(\frac{3\pi}{4} \right )=\frac{1}{2}$

$\cos\left(\frac{3\pi}{4} \right )=-\frac{1}{\sqrt{2}}$

$\cos\left(\frac{3\pi}{4} \right )=\frac{1}{\sqrt{2}}$

$\cos\left(\frac{3\pi}{4} \right )=-\sqrt{2}$

Correct answer:

$\cos\left(\frac{3\pi}{4} \right )=-\frac{1}{\sqrt{2}}$

Explanation:

This question tests one's ability to recognize and use the unit circle to calculate the exact trigonometric value.

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: Recall the unit circle.

Screen shot 2016 01 14 at 10.52.42 am

Step 2: Identify the (x,y) coordinate pair that represents the extension of $\theta = \frac{3\pi}{4}$ .

$\theta = \frac{3\pi}{4}\Rightarrow \left(-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \right )$

Step 3: Calculate the exact value of $\cos\left(\frac{3\pi}{4} \right )$ .

Recall that,

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

therefore,

$\left(-\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}\right)=\left(\cos\left(\frac{3\pi}{4}\right),\sin\left(\frac{3\pi}{4}\right)\right)$

$\cos\left(\frac{3\pi}{4} \right )=-\frac{1}{\sqrt{2}}$ .

Report an Error

Example Question #42 : Trigonometric Functions

Find the following trigonometric exact value.

$\sin\left(\frac{3\pi}{4} \right )$

Possible Answers:

$\sin\left(\frac{3\pi}{4} \right )=\sqrt{2}$

$\sin\left(\frac{3\pi}{4} \right )=\frac{1}{\sqrt{2}}$

$\sin\left(\frac{3\pi}{4} \right )=-\frac{1}{\sqrt{2}}$

$\sin\left(\frac{3\pi}{4} \right )=-\frac{1}{2}$

$\sin\left(\frac{3\pi}{4} \right )=\frac{1}{2}$

Correct answer:

$\sin\left(\frac{3\pi}{4} \right )=\frac{1}{\sqrt{2}}$

Explanation:

This question tests one's ability to recognize and use the unit circle to calculate the exact trigonometric value.

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: Recall the unit circle.

Screen shot 2016 01 14 at 10.52.42 am

Step 2: Identify the (x,y) coordinate pair that represents the extension of $\theta = \frac{3\pi}{4}$ .

$\theta = \frac{3\pi}{4}\Rightarrow \left(-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \right )$

Step 3: Calculate the exact value of $\sin\left(\frac{3\pi}{4} \right )$ .

Recall that,

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

therefore,

$\left(-\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}\right)=\left(\cos\left(\frac{3\pi}{4}\right),\sin\left(\frac{3\pi}{4}\right)\right)$

$\sin\left(\frac{3\pi}{4} \right )=\frac{1}{\sqrt{2}}$ .

Report an Error

Example Question #1 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

What is the period of the following function?

$y=\sin(2x)$

Possible Answers:

$\frac{\pi}{2}$

$2\pi$

$\pi$

Correct answer:

$\pi$

Explanation:

This question is testing one's ability to identify the periodicity of a trigonometric function. This requires the understanding of trigonometric functions and their graphical and algebraic characteristics.

For the purpose of Common Core Standards, "Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline" falls within the Cluster B of "Model Periodic Phenomena with Trigonometric Functions" concept (CCSS.MATH.CONTENT.HSF-TF.B.5).

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: Write the general form of trigonometric shifts.

F(x)=af(bx-c)+d

where

$\\F(x)=\textup{New function after shift} \\a=\textup{Amplitude} \\b=\textup{period}\rightarrow \frac{2\pi}{|B|} \\ \\c=\textup{Horizontal shift} \\ d=\textup{Vertical shift} \\f(x)=\textup{Trigonometric function}$

Step 2: Algebraically identify the period.

Given the function

$y=\sin(2x)$

identify the variables of the general form.

$\\f(x)=\sin \\a=1 \\b=2\rightarrow \frac{2\pi}{|2|}=\pi \\c=0 \\d=0$

Step 3: Graph the trigonometric function to verify.

Screen shot 2016 01 19 at 6.51.48 am

The graph above verifies that the period of this function is $\pi$ because the flow of the graph only begins to repeat its cycle after $\pi$ units on the - axis.

Report an Error

Example Question #2 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

What is the amplitude of the following function?

$y=2\sin(x)$

Possible Answers:

$\frac{\pi}{2}$

$2\pi$

Correct answer:

Explanation:

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: Write the general form of trigonometric shifts.

F(x)=af(bx-c)+d

where

Step 2: Algebraically identify the amplitude.

Given the function

$y=2\sin(x)$

identify the variables of the general form.

$\\f(x)=\sin \\a=2 \\b=1\rightarrow \frac{2\pi}{|1|}=2\pi \\c=0 \\d=0$

Step 3: Graph the trigonometric function to verify.

The graph above verifies that the amplitude of this function is two because the range of the function on the graph goes from negative two to positive two meaning the distance from zero at its highest peak or lowest valley is two.

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 10 11 Next →

View Tutors

Mary
Certified Tutor

St Martins College, Bachelor of Education, Education of Individuals in Elementary Special Education Programs.

View Tutors

Joshua
Certified Tutor

Arizona State University, Bachelor of Science, Biology, General.

View Tutors

Ishaan
Certified Tutor

Georgia Institute of Technology-Main Campus, Bachelor of Science, Computer Science.

All Common Core: High School - Functions Resources

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

Popular Subjects

Algebra Tutors in Los Angeles, Biology Tutors in Denver, GMAT Tutors in San Diego, Statistics Tutors in Phoenix, Calculus Tutors in Houston, Chemistry Tutors in Philadelphia, LSAT Tutors in Seattle, French Tutors in Phoenix, Reading Tutors in Seattle, Biology Tutors in New York City

Popular Courses & Classes

ACT Courses & Classes in Denver, SAT Courses & Classes in Atlanta, ISEE Courses & Classes in New York City, ACT Courses & Classes in Washington DC, SAT Courses & Classes in New York City, SSAT Courses & Classes in Houston, GMAT Courses & Classes in Boston, SAT Courses & Classes in Denver, ISEE Courses & Classes in Denver, SSAT Courses & Classes in Chicago

Popular Test Prep

ACT Test Prep in Denver, SSAT Test Prep in Seattle, MCAT Test Prep in Seattle, ACT Test Prep in Atlanta, ISEE Test Prep in New York City, GRE Test Prep in Houston, GRE Test Prep in Los Angeles, SAT Test Prep in Houston, ACT Test Prep in Washington DC, MCAT 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

Common Core: High School - Functions : Trigonometric Functions

Study concepts, example questions & explanations for Common Core: High School - Functions

All Common Core: High School - Functions Resources

Example Questions

Example Question #5 : Symmetry And Periodicity Of Trigonometric Functions: Ccss.Math.Content.Hsf.Tf.B.4

Example Question #6 : Symmetry And Periodicity Of Trigonometric Functions: Ccss.Math.Content.Hsf.Tf.B.4

Example Question #7 : Symmetry And Periodicity Of Trigonometric Functions: Ccss.Math.Content.Hsf.Tf.B.4

Example Question #8 : Symmetry And Periodicity Of Trigonometric Functions: Ccss.Math.Content.Hsf.Tf.B.4

Example Question #9 : Symmetry And Periodicity Of Trigonometric Functions: Ccss.Math.Content.Hsf.Tf.B.4

Example Question #10 : Symmetry And Periodicity Of Trigonometric Functions: Ccss.Math.Content.Hsf.Tf.B.4

Example Question #41 : Trigonometric Functions

Example Question #42 : Trigonometric Functions

Example Question #1 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

Example Question #2 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

All Common Core: High School - Functions Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: