Call Now to Set Up Tutoring:

(888) 888-0446

Trigonometry : Sum, Difference, and Product Identities

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 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines

True or false:

$\sin x + \sin y = \sin (x + y)$ .

Possible Answers:

Cannot be determined

False

True

Correct answer:

False

Explanation:

The sum of sines is given by the formula $\sin x + \sin y = \2\sin ((x + y)/2) * \cos((x - y)/2)$ .

Report an Error

Example Question #2 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines

True or false: $\sin x - \sin y = \sin (x - y)$ .

Possible Answers:

False

True

Cannot be determined

Correct answer:

False

Explanation:

The difference of sines is given by the formula $\sin x - \sin y = \2\sin ((x - y)/2) * \cos((x + y)/2)$ .

Report an Error

Example Question #1 : Sum, Difference, And Product Identities

True or false: $\cos x + \cos y = \cos (x + y)$ .

Possible Answers:

Cannot be determined

True

False

Correct answer:

False

Explanation:

The sum of cosines is given by the formula $\cos x + \cos y = 2\cos ((x + y)/2) * \cos((x - y)/2)$ .

Report an Error

Example Question #2 : Sum, Difference, And Product Identities

True or false: $\cos x - \cos y = \cos (x - y)$ .

Possible Answers:

False

True

Cannot be determined

Correct answer:

False

Explanation:

The difference of cosines is given by the formula $\cos x - \cos y = 2\sin ((x + y)/2) * \sin((y - x)/2)$ .

Report an Error

Example Question #3 : Sum, Difference, And Product Identities

Which of the following correctly demonstrates the compound angle formula?

Possible Answers:

$\sin(x + y) = sinxcosy - cosxsiny$

$\sin(x + y) = sinxsiny - cosxcosy$

$\sin(x - y) = sinxsiny - cosxcosy$

$\sin(x - y) = sinxcosy - cosxsiny$

Correct answer:

$\sin(x - y) = sinxcosy - cosxsiny$

Explanation:

The compound angle formula for sines states that $\sin(x +- y) = sinxcosy +- cosxsiny$ .

Report an Error

Example Question #1 : Sum, Difference, And Product Identities

Which of the following correctly demonstrates the compound angle formula?

Possible Answers:

$\cos(x - y) = sinxcosy - cosxsiny$

$\cos(x - y) = sinxsiny - cosxcosy$

$\cos(x + y) = sinxcosy - cosxsiny$

$\cos(x + y) = sinxsiny - cosxcosy$

Correct answer:

$\cos(x + y) = sinxsiny - cosxcosy$

Explanation:

The compound angle formula for cosines states that $\cos(x +- y) = sinxsiny -+ cosxcosy$ .

Report an Error

Example Question #7 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines

Simplify by applying the compound angle formula:

(1/2)(sinxcosy - cosxsiny + sinxcosy + cosxsiny)

Possible Answers:

cosxsiny

sinxcosy

sinxsiny

cosxcosy

Correct answer:

sinxcosy

Explanation:

Using the compound angle formula, we can rewrite each half of the non-coefficient terms in the given expression. Given that $\sin (x - y) = sinxcosy - cosxsiny$ and $\sin (x + y) = sinxcosy + cosxsiny$ , substitution yields the following:

(1/2)(sinxcosy - cosxsiny + sinxcosy + cosxsiny)

(1/2)(sin(x - y) + sin(x + y))

This is the formula for the product of sine and cosine, $sinxcosy = (1/2)(\sin(x - y) + \sin(x + y))$ .

Report an Error

Example Question #8 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines

Simplify by applying the compound angle formula:

(1/2)(sinxsiny + cosxcosy + sinxsiny - cosxcosy)

Possible Answers:

sinxsiny

sinxcosy

cosxcosy

cosxsiny

Correct answer:

cosxcosy

Explanation:

Using the compound angle formula, we can rewrite each half of the non-coefficient terms in the given expression. Given that $\cos(x - y) = sinxsiny + cosxcosy$ and $\cos(x + y) = sinxsiny - cosxcosy$ , substitution yields the following:

(1/2)(sinxsiny + cosxcosy + sinxsiny - cosxcosy)

$(1/2)(\cos(x - y) + \cos(x + y))$

This is the formula for the product of two cosines, $cosxcosy = (1/2)(\cos(x - y) + \cos(x + y))$ .

Report an Error

Example Question #9 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines

Using $\sin(90 - x) = \cos x$ and the formula for the sum of two sines, rewrite the sum of cosine and sine:

$\cos x + \sin x$

Possible Answers:

$2\sin(45) * \cos(45 - x)$

$2\sin(90) * \cos(90 - x)$

$\sin(90) * \cos(90 - x)$

$\sin(45) * \cos(45 - x)$

Correct answer:

$2\sin(45) * \cos(45 - x)$

Explanation:

Substitute $\sin(90 - x)$ for $\cos x$ :

$\cos x + \sin x$

$\sin(90 - x) + \sin x$

Apply the formula for the sum of two sines, $\sin x + \sin y = 2\sin ((x + y)/2) * \cos((x - y)/2)$ :

$\sin(90 - x) + \sin x$

$2\sin((90 - x + x)/2) * \cos((90 - x - x)/2)$

$2\sin(45) * \cos(45 - x)$

Report an Error

Example Question #10 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines

Using $\sin(90 - x) = \cos x$ and the formula for the difference of two sines, rewrite the difference of cosine and sine:

$\cos x - \sin x$

Possible Answers:

$\sin(45) * \cos(45 - x)$

$\sin(45 - x) * \cos(45)$

$2\sin(45) * \cos(45 - x)$

$2\sin(45 - x) * \cos(45)$

Correct answer:

$2\sin(45 - x) * \cos(45)$

Explanation:

Substitute $\sin(90 - x)$ for $\cos x$ :

$\cos x - \sin x$

$\sin(90 - x) - \sin x$

Apply the formula for the difference of two sines, $\sin x - \sin y = 2\sin((x - y)/2) * \cos((x + y)/2)$ .

$\sin(90 - x) - \sin x$

$2\sin((90 - x - x)/2) * \cos((90 - x + x)/2)$

$2\sin(45 - x) * \cos(45)$

Report an Error

View Trigonometry Tutors

Ivory
Certified Tutor

Hopkinsville Community College, Associate, Associates in Science. Western Kentucky University, Bachelor in Arts, Psychology.

View Trigonometry Tutors

Ian
Certified Tutor

Lipscomb University, Bachelor of Science, Biology, General.

View Trigonometry Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

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

SSAT Courses & Classes in Denver, MCAT Courses & Classes in San Diego, SAT Courses & Classes in Houston, LSAT Courses & Classes in Atlanta, SAT Courses & Classes in Philadelphia, SSAT Courses & Classes in Washington DC, Spanish Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Houston, SSAT Courses & Classes in New York City, ISEE Courses & Classes in Boston

Popular Test Prep

MCAT Test Prep in Washington DC, SAT Test Prep in Atlanta, GRE Test Prep in Denver, ACT Test Prep in Phoenix, MCAT Test Prep in Miami, SSAT Test Prep in San Diego, SAT Test Prep in Los Angeles, SAT Test Prep in San Diego, ISEE Test Prep in Los Angeles, LSAT Test Prep in Boston

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 : Sum, Difference, and Product Identities

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #1 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines

Example Question #2 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines

Example Question #1 : Sum, Difference, And Product Identities

Example Question #2 : Sum, Difference, And Product Identities

Example Question #3 : Sum, Difference, And Product Identities

Example Question #1 : Sum, Difference, And Product Identities

Example Question #7 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines

Example Question #8 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines

Example Question #9 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines

Example Question #10 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines

All Trigonometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: