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: Prove Addition and Subtraction Formula for Trigonometric Functions: CCSS.Math.Content.HSF-TF.C.9

Using the addition formula for sine and special reference angles calculate,

$\sin(105^\circ)$ .

$\sin(105^\circ)=\frac{\sqrt{8}}{2}$

$\sin(105^\circ)=\frac{2+\sqrt{6}}{2}$

$\sin(105^\circ)=\frac{\sqrt{2}+\sqrt{6}}{4}$

$\sin(105^\circ)=\frac{\sqrt{2}}{2}$

$\sin(105^\circ)=\frac{\sqrt{2}+\sqrt{6}}{2}$

Report an Error Copyright Notice

Flashcards: Prove Addition and Subtraction Formula for Trigonometric Functions: CCSS.Math.Content.HSF-TF.C.9

Using the addition formula for sine and special reference angles calculate,

$\sin(105^\circ)$ .

Your answer:

$\sin(105^\circ)=\frac{\sqrt{8}}{2}$

Your answer:

$\sin(105^\circ)=\frac{2+\sqrt{6}}{2}$

Your answer:

$\sin(105^\circ)=\frac{\sqrt{2}}{2}$

Your answer:

$\sin(105^\circ)=\frac{\sqrt{2}+\sqrt{6}}{2}$

Correct answer:

$\sin(105^\circ)=\frac{\sqrt{2}+\sqrt{6}}{4}$

Explanation:

This type of question tests the deep understanding of geometry, right triangles, trigonometry, and dealing with proofs. Questions such as these are not designed to be tested but instead are used to build knowledge that will help in higher level mathematics courses.

For the purpose of Common Core Standards, "prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems", falls within the Cluster C of "prove and apply trigonometric identities" (CCSS.MATH.CONTENT.HSF.TF.C).

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: Break the angle into two angles that correspond to special reference angles.

$105^\circ=60^\circ+45^\circ$

Step 2: Write the general addition formula for sine.

$\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)$

Step 3: Substitute in the reference angles into the general addition formula for sine.

$\\a=60^\circ \\b=45^\circ$

$\\ \sin(60^\circ+45^\circ)=\sin(60^\circ)\cos(45^\circ)+\cos(60^\circ)\sin(45^\circ) \\\sin(60^\circ+45^\circ)=\frac{\sqrt{3}}{2}\times\frac{1}{\sqrt{2}}+\frac{1}{2}\times\frac{1}{\sqrt{2}} \\ \\ \sin(60^\circ+45^\circ)=\frac{\sqrt{3}}{2\sqrt{2}}+\frac{1}{2\sqrt{2}} \\ \\ \sin(60^\circ+45^\circ)=\frac{1+\sqrt{3}}{2\sqrt{2}}$

To rationalize the denominator multiply the numerator and denominator by the square root of two.

$\\ \sin(60^\circ+45^\circ)=\frac{\sqrt{2}+\sqrt{6}}{4} \\ \\ \sin(105^\circ)=\frac{\sqrt{2}+\sqrt{6}}{4}$

Flashcards: Prove Addition and Subtraction Formula for Trigonometric Functions: CCSS.Math.Content.HSF-TF.C.9

Using the addition formula for sine and special reference angles calculate,

$\sin(75^\circ)$ .

$\sin(75^\circ)=\frac{\sqrt{3}}{2\sqrt2}$

$\sin(75^\circ)=\frac{1+\sqrt{3}}{2}$

$\sin(75^\circ)=\frac{1+\sqrt{3}}{\sqrt2}$

$\sin(75^\circ)=\frac{1+\sqrt{3}}{2\sqrt2}$

$\sin(75^\circ)=\frac{1}{2\sqrt2}$

Report an Error Copyright Notice

Flashcards: Prove Addition and Subtraction Formula for Trigonometric Functions: CCSS.Math.Content.HSF-TF.C.9

Using the addition formula for sine and special reference angles calculate,

$\sin(75^\circ)$ .

Your answer:

$\sin(75^\circ)=\frac{\sqrt{3}}{2\sqrt2}$

Your answer:

$\sin(75^\circ)=\frac{1+\sqrt{3}}{2}$

Your answer:

$\sin(75^\circ)=\frac{1+\sqrt{3}}{\sqrt2}$

Your answer:

$\sin(75^\circ)=\frac{1}{2\sqrt2}$

Correct answer:

$\sin(75^\circ)=\frac{1+\sqrt{3}}{2\sqrt2}$

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: Break the angle into two angles that correspond to special reference angles.

$75^\circ=30^\circ+45^\circ$

Step 2: Write the general addition formula for sine.

$\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)$

Step 3: Substitute in the reference angles into the general addition formula for sine.

$\\a=30^\circ \\b=45^\circ$

$\\ \sin(30^\circ+45^\circ)=\sin(30^\circ)\cos(45^\circ)+\cos(30^\circ)\sin(45^\circ) \\\sin(30^\circ+45^\circ)=\frac{1}{2}\times\frac{1}{\sqrt{2}}+\frac{\sqrt3}{2}\times\frac{1}{\sqrt{2}} \\ \\ \sin(30^\circ+45^\circ)=\frac{1}{2\sqrt{2}}+\frac{\sqrt{3}}{2\sqrt{2}} \\ \\ \sin(30^\circ+45^\circ)=\frac{1+\sqrt{3}}{2\sqrt{2}}$

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

Cassandra
Certified Tutor

University of Virginia-Main Campus, Bachelor in Arts, English.

View Tutors

Salinah
Certified Tutor

SUNY at Purchase College, Bachelor of Science, Biology, General.

View Tutors

Adil
Certified Tutor

Pace University-New York, Master of Arts, Accounting and Business Management. University of the Cumberlands, Master of Scienc...

Popular Subjects

ISEE Tutors in Denver, GRE Tutors in Dallas Fort Worth, Biology Tutors in Phoenix, Physics Tutors in Philadelphia, ISEE Tutors in San Diego, ACT Tutors in Denver, GRE Tutors in San Francisco-Bay Area, French Tutors in New York City, MCAT Tutors in Miami, ISEE Tutors in Houston

Popular Courses & Classes

SAT Courses & Classes in Houston, SAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Washington DC, ACT Courses & Classes in Chicago, SAT Courses & Classes in Chicago, SSAT Courses & Classes in Chicago, SSAT Courses & Classes in Miami, LSAT Courses & Classes in Atlanta, GRE Courses & Classes in Atlanta, MCAT Courses & Classes in New York City

Popular Test Prep

ISEE Test Prep in Los Angeles, MCAT Test Prep in New York City, MCAT Test Prep in Atlanta, GRE Test Prep in Atlanta, GRE Test Prep in Los Angeles, MCAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Atlanta, SAT Test Prep in San Diego, SSAT Test Prep in Phoenix, MCAT Test Prep in Seattle

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: Prove Addition and Subtraction Formula for Trigonometric Functions: CCSS.Math.Content.HSF-TF.C.9

Flashcards: Prove Addition and Subtraction Formula for Trigonometric Functions: CCSS.Math.Content.HSF-TF.C.9

Flashcards: Prove Addition and Subtraction Formula for Trigonometric Functions: CCSS.Math.Content.HSF-TF.C.9

Flashcards: Prove Addition and Subtraction Formula for Trigonometric Functions: CCSS.Math.Content.HSF-TF.C.9

Report an issue with this question