Call Now to Set Up Tutoring:

(888) 888-0446

Trigonometry : Identities of Inverse Operations

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 : Identities Of Inverse Operations

Simplify using identities. Leave no fractions in your answer.

$\sec \theta(cos\theta\sin\theta) - \csc\theta\tan\theta$

Possible Answers:

$\sin\theta - \cos\theta$

$\cos\theta - \sec\theta$

$\cos\theta-\sin\theta$

$\sin\theta - \sec\theta$

$\cot\theta$

Correct answer:

$\sin\theta - \sec\theta$

Explanation:

The easiest first step is to simplify our inverse identities:

$\sec \theta(cos\theta\sin\theta) - \csc\theta\tan\theta = \bigg(\frac{1}{cos\theta}\bigg)cos\theta\sin\theta-\bigg(\frac{1}{\sin\theta}\bigg)\bigg(\frac{sin\theta}{\cos\theta}\bigg)$

Cross cancelling, we end up with

$\bigg(\frac{1}{cos\theta}\bigg)cos\theta\sin\theta-\bigg(\frac{1}{\sin\theta}\bigg)\bigg(\frac{\sin\theta}{\cos\theta}\bigg)=\sin\theta-\frac{1}{\cos\theta}$

Finally, eliminate the fraction:

$\sin\theta - \frac{1}{\cos\theta}= \sin\theta-\sec\theta$

Thus,

$\sec \theta(cos\theta\sin\theta) - \csc\theta\tan\theta = \sin\theta - \sec\theta$

Report an Error

Example Question #2 : Identities Of Inverse Operations

Simplify each expression below. Your answer should have (at most) one trigonometric function and no fractions.

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

Possible Answers:

cos^2(x)

$\frac{cos^2(x)}{sin^2(x)}$

cot^2(x)

tan^2(x)

Correct answer:

cot^2(x)

Explanation:

Using the quotient identities for trig functions, you can rewrite,

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

and

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

Then the fraction becomes

$\frac{cot(x)}{tan(x)}=\frac{cos^2(x)}{sin^2(x)}=cot^2(x)$

Report an Error

Example Question #3 : Identities Of Inverse Operations

Simplify each expression below. Your answer should have (at most) one trigonometric function and no fractions.

(sin^2(x)-1)(1-sin^2(x))

Possible Answers:

1-sin^2(x)

-cos^2(x)(1-sin^2(x))

-cos^4(x)

cos^4(x)

Correct answer:

-cos^4(x)

Explanation:

Use the Pythagorean Identities:

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

and

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

Thus the expression becomes,

(-cos^2(x))(cos^2(x))=-cos^4(x) .

Report an Error

Example Question #4 : Identities Of Inverse Operations

Simplify each expression below. Your answer should have (at most) one trigonometric function and no fractions.

(cot(x) - csc(x))(cot(x)+csc(x))

Possible Answers:

sin^2(x)

cos^2(x)

Correct answer:

Explanation:

Use the distributive property (FOIL method) to simplify the expression.

(cot(x) - csc(x))(cot(x)+csc(x))

=cot^2(x)-cot(x)csc(x)+cot(x)csc(x)-csc^2(x)

=cot^2(x)-csc^2(x)

Using Pythagorean Identities:

=cot^2(x)-csc^2(x)=-1 .

Report an Error

Example Question #5 : Identities Of Inverse Operations

Simplify each expression below. Your answer should have (at most) one trigonometric function and no fractions.

$(sin^2(x)+cos^2(x)) - \frac{cos^2(x)}{(1-sin(x))}$

Possible Answers:

2-sin(x)

-sin(x)

sin(x)

2+sin(x)

Correct answer:

-sin(x)

Explanation:

First, simplify the first term in the expression to 1 because of the Pythagorean Identity.

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

Then, simplify the second term to

$\frac{(1 - sin^2x)}{(1 - sinx)}$ .

This reduces to

$\frac{(1-sinx)(1+sinx)}{1-sinx}=1+sin(x)$ .

The expression is now,

1 - (1+sinx) .

Distribute the negative and get,

-sinx .

Report an Error

Example Question #72 : Trigonometric Identities

Solve each question over the interval $0 < x < 2\pi$

tanx = cotx

Possible Answers:

$0, 2\pi$

$\frac{\pi}{4}, \frac{5\pi}{4}$

$\frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}$

$\frac{\pi}{2}, \frac{3\pi}{2}, 2\pi$

Correct answer:

$\frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}$

Explanation:

Divide both sides by cotx to get tan^2x = 1 .

Take the square root of both sides to get that tanx = 1 and tanx = -1 .

The angles for which this is true (this is taking the arctan) are every angle when sinx = cosx and sinx = -cosx .

These angles are all the multiples of $\frac{\pi}{4}$ .

Report an Error

Example Question #7 : Identities Of Inverse Operations

tan(x) can be stated as all of the following except...

Possible Answers:

tan(-x)

$cot(x)^{-1}$

$cot(\frac{\pi}{2} - x)$

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

-tan(-x)

Correct answer:

tan(-x)

Explanation:

Let's look at these individually:

$\frac{sin(x)}{cos(x)}$ is true by definition, as is $cot(x)^{-1}$ .

$cot(\frac{\pi}{2} - x)$ is also true because of a co-function identity.

This leaves two - and we can tell which of these does not work using the fact that tan(-x) = -tan(x) , which means that tan(-x) is our answer.

Report an Error

View Trigonometry Tutors

Abhisek
Certified Tutor

University of Florida, Bachelor of Engineering, Computer Science.

View Trigonometry Tutors

Yuliya
Certified Tutor

University of Maryland-College Park, Bachelor of Science, Mathematics. George Washington University, Masters in Education, Ed...

View Trigonometry Tutors

Mark
Certified Tutor

Murray State University, Bachelor of Science, Mathematics.

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, SSAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in New York City, SAT Courses & Classes in Atlanta, GRE Courses & Classes in Chicago, GRE Courses & Classes in Los Angeles, LSAT Courses & Classes in Chicago, SSAT Courses & Classes in New York City, SSAT Courses & Classes in Seattle, MCAT Courses & Classes in Denver

Popular Test Prep

GMAT Test Prep in New York City, GRE Test Prep in Seattle, GRE Test Prep in Miami, ISEE Test Prep in Denver, MCAT Test Prep in Seattle, ISEE Test Prep in San Francisco-Bay Area, GRE Test Prep in Chicago, MCAT Test Prep in Atlanta, MCAT Test Prep in Miami, SSAT Test Prep in New York City

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 : Identities of Inverse Operations

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #1 : Identities Of Inverse Operations

Example Question #2 : Identities Of Inverse Operations

Example Question #3 : Identities Of Inverse Operations

Example Question #4 : Identities Of Inverse Operations

Example Question #5 : Identities Of Inverse Operations

Example Question #72 : Trigonometric Identities

Example Question #7 : Identities Of Inverse Operations

All Trigonometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: