Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Trigonometric Identities

Study concepts, example questions & explanations for Precalculus

Create An Account

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Trigonometric Identities

According to the trigonometric identities, 1+cot^2(x)=?

Possible Answers:

$\frac{sin(x)}{cos(x)}$

tan(x)

csc^2(x)

$\frac{1}{tan(x)}$

Correct answer:

csc^2(x)

Explanation:

The trigonometric identity 1+cot^2(x)=csc^2(x) , is an important identity to memorize.

Some other identities that are important to know are:

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

$cot(x)=\frac{1}{tan(x)}$

sin^2(x)+cos^2(x)=1

Report an Error

Example Question #1 : Sum And Difference Identities

Use the sum or difference identity to find the exact value: $sin165^\circ$

Possible Answers:

$\frac{\sqrt{6}+\sqrt{2}}{4}$

$\frac{\sqrt{2}-\sqrt{6}}{4}$

$\frac{\sqrt{6}}{4}$

$\frac{\sqrt{6}-\sqrt{2}}{4}$

$\frac{1}{2}$

Correct answer:

$\frac{\sqrt{6}-\sqrt{2}}{4}$

Explanation:

Again, here we break up the 165 into 135+30 and solve using the sin identity: $sin135\cdot cos30+cos135\cdot sin30\rightarrow \frac{\sqrt{2}}{2}\cdot \frac{\sqrt{3}}{2}+\frac{-\sqrt{2}}{2}\cdot \frac{1}{2}\rightarrow \frac{\sqrt{6}-\sqrt{2}}{4}$

Report an Error

Example Question #1 : Sum And Difference Identities

Is the following equation an identity? $sin(x-\pi)=sin(x)$

Possible Answers:

It cannot be determined from the given information.

No it is not an identity.

Yes it is an identity.

Correct answer:

No it is not an identity.

Explanation:

$sin(x-\pi)=sinx\rightarrow sinxcos\pi-cosxsin\pi=sinx\rightarrow sinx\cdot (-1)-cosx\cdot (0)\rightarrow -sinx-0=sinx\rightarrow -sinx\neq sinx$

and so this is again not an identity

Report an Error

Example Question #1 : Trigonometric Identities

Is the following equation an identity? $\sin \left ( x-\pi \right )=\sin \left ( x \right )$ ?

Possible Answers:

No it is not an identity

The question cannot be answered based on the information provided.

Yes it is an identity

Correct answer:

No it is not an identity

Explanation:

$\sin \left ( x-\pi \right )=\sin x\rightarrow \sin x\cos \pi -\cos x\sin \pi = \sin x\rightarrow \sin x\cdot \left ( -1 \right )-\cos x\cdot \left ( 0 \right )\rightarrow -\sin x-0=\sin x\neq \sin x$

Therefore, this is not an identity.

Report an Error

Example Question #1 : Trigonometric Identities

Use the sum or difference identity to find the exact value: $cos255^\circ$

Possible Answers:

$\frac{1}{2}$

$\frac{2\sqrt{2}}{4}$

$\frac{\sqrt{2}-\sqrt{6}}{4}$

$\frac{-1}{2}$

$\frac{\sqrt{2}+\sqrt{6}}{4}$

Correct answer:

$\frac{\sqrt{2}-\sqrt{6}}{4}$

Explanation:

Using the identity, we can break up the 255 into and then solve: $cos300\cdot cos45+sin300\cdot sin45\rightarrow \frac{1}{2}\cdot \frac{\sqrt{2}}{2}+\frac{-\sqrt{3}}{2}\cdot \frac{\sqrt{2}}{2}\rightarrow \frac{\sqrt{2}-\sqrt{6}}{4}$

Report an Error

Example Question #2 : Sum And Difference Identities

Is the following equation an identity? $cos(x-\pi)=cos(x)$

Possible Answers:

No it is not an identity.

Yes it is an identity.

It cannot be determined from the given information.

Correct answer:

No it is not an identity.

Explanation:

$cos(x-\pi)=cos(x)\rightarrow cosxcos\pi+sinxsin\pi=cosx\rightarrow cosx(-1)+sinx(0)=cosx\rightarrow -cosx\neq cosx$

and due to this inequality, this is not an identity

Report an Error

Example Question #3 : Trigonometric Identities

Use the sum or difference identity to find the exact value: $\cos 255^{\circ}$

Possible Answers:

$-\frac{1}{2}$

$\frac{\sqrt{2}-\sqrt{6}}{4}$

$\frac{1}{2}$

$\frac{2\sqrt{2}}{4}$

$\frac{\sqrt{2}+\sqrt{6}}{4}$

Correct answer:

$\frac{\sqrt{2}-\sqrt{6}}{4}$

Explanation:

Using the identity, we can break up the 255 into 300-45 and then solve: $\cos 300\cdot \cos 45+\sin 300\cdot \sin 45\rightarrow \frac{1}{2}\cdot \frac{\sqrt{2}}{2}+\frac{-\sqrt{3}}{2}\cdot \frac{\sqrt{2}}{2}\rightarrow \frac{\sqrt{2}-\sqrt{6}}{4}$ and so the correct answer is $\frac{\sqrt{2}-\sqrt{6}}{4}$ .

Report an Error

Example Question #1 : Sum And Difference Identities For Cosine

Is the following equation an identity?

$\cos \left ( x-\pi \right )=\cos \left ( x \right )$

Possible Answers:

The answer cannot be determined from the information provided.

Yes it is an identity

No it is not an identity

Correct answer:

No it is not an identity

Explanation:

$\cos \left ( x-\pi \right )=\cos \left ( x \right )\rightarrow \cos x\cos \pi +\sin x\sin \pi =\cos x\rightarrow \cos x(-1)+\sin x(0)=\cos x\rightarrow -\cos x\neq \cos x$

Due to this inequality, this is not an identity.

Report an Error

Example Question #9 : Sum And Difference Identities

Use the sum or difference identity to find the exact value of $\sin 165^{\circ}$ .

Possible Answers:

$\frac{1}{2}$

$\frac{\sqrt{6}}4{}$

$\frac{\sqrt{2}-\sqrt{6}}{4}$

$\frac{\sqrt{6}-\sqrt{2}}{4}$

$\frac{\sqrt{6}+\sqrt{2}}{4}$

Correct answer:

$\frac{\sqrt{6}-\sqrt{2}}{4}$

Explanation:

Here we break up the 165 into 135+30 and solve using the sin identity: $\sin 135\cdot \cos 30+\cos 135\cdot \sin 30\rightarrow \frac{\sqrt{2}}2{}\cdot \frac{\sqrt{3}}2{}+\frac{-\sqrt{2}}2{}\cdot \frac{1}{2}\rightarrow \frac{\sqrt{6}-\sqrt{2}}{4}$ and so here the credited answer is $\frac{\sqrt{6}-\sqrt{2}}{4}$ .

Report an Error

Example Question #211 : Pre Calculus

Use trigonometric identities to solve the following equation for $\theta$ :

$tan^2\theta + sec^2\theta = 1$

Possible Answers:

$\theta = \pi/3+ n$

$\theta = \pi/4+ n\pi$

$\theta = \pi/2+ n\pi$

$\theta= n\pi$

Correct answer:

$\theta= n\pi$

Explanation:

Use the trigonometric identities to switch sec into terms of tan:

$tan^2\theta + sec^2\theta = tan^2\theta + (tan^2 \theta + 1) = 2tan^2\theta + 1 = 1$

hence,

$2tan^2\theta = 0$

So we have $\tan \theta = 0$ , making $\theta= n \pi$

Therefore the solution is $\theta = n \pi$ for n being any integer.

Report an Error

View Pre-Calculus Tutors

Abhisek
Certified Tutor

University of Florida, Bachelor of Engineering, Computer Science.

View Pre-Calculus Tutors

Anabel
Certified Tutor

UDELAR, Diploma, Chemistry. IPA, Bachelor of Education, Mathematics.

View Pre-Calculus Tutors

Michael
Certified Tutor

Cleveland State University, Bachelor of Science, Mathematics.

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GMAT Tutors in Atlanta, LSAT Tutors in Miami, LSAT Tutors in Dallas Fort Worth, Reading Tutors in Chicago, Algebra Tutors in Denver, LSAT Tutors in New York City, ACT Tutors in Dallas Fort Worth, ACT Tutors in Miami, ACT Tutors in Chicago, Math Tutors in San Diego

Popular Courses & Classes

SSAT Courses & Classes in Phoenix, SSAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Boston, MCAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in New York City, SAT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Denver, LSAT Courses & Classes in Atlanta, ISEE Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in New York City

Popular Test Prep

MCAT Test Prep in San Diego, GRE Test Prep in Dallas Fort Worth, ACT Test Prep in New York City, ISEE Test Prep in Denver, MCAT Test Prep in Phoenix, GMAT Test Prep in Atlanta, LSAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Dallas Fort Worth, GMAT Test Prep in Seattle, GRE Test Prep in Los Angeles

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

Precalculus : Trigonometric Identities

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Trigonometric Identities

Example Question #1 : Sum And Difference Identities

Example Question #1 : Sum And Difference Identities

Example Question #1 : Trigonometric Identities

Example Question #1 : Trigonometric Identities

Example Question #2 : Sum And Difference Identities

Example Question #3 : Trigonometric Identities

Example Question #1 : Sum And Difference Identities For Cosine

Example Question #9 : Sum And Difference Identities

Example Question #211 : Pre Calculus

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: