Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Trigonometric Functions

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 #131 : Trigonometric Functions

Simplify.

$1-\tan x(\csc x)$

Possible Answers:

$1-\sec x$

$\tan^2 x$

None of these answers are correct.

$\sin^2x$

Correct answer:

$1-\sec x$

Explanation:

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

$\frac{1}{\sin x}=\csc x$

Given these identities...

$1-\tan x(\csc x)$

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

$1-\frac{1}{\cos x}$

$1- \sec x$

Report an Error

Example Question #132 : Trigonometric Functions

Simplify $\frac{\sin (x)}{1-\cos (x)}-\cot(x)$ completely.

Possible Answers:

$-\sec (x)$

$-\tan (x)$

$1-\tan(x)$

$\csc (x)$

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

Correct answer:

$\csc (x)$

Explanation:

First simplify the fraction

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

by multiplying it by its conjugate

$\frac{1+\cos (x)}{1+\cos (x)}$ .

After doing so, continue simplying:

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

Report an Error

Example Question #133 : Trigonometric Functions

Fully simplify.

Simplify:

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

Possible Answers:

$\cos^2 x$

$\sin ^2 x$

$\sin x + \cos x$

None of these answers are correct.

Correct answer:

$\sin ^2 x$

Explanation:

$\sin^2 x + \cos^2 x = 1$

$1+ \cot^2x= \csc^2 x$

Given the above identities:

$\frac{(\sin ^2 x+ \cos^2 x)}{(1+ \cot^2 x)}=\frac{1}{\csc^2 x}=\sin^2x$

Report an Error

Example Question #134 : Trigonometric Functions

Simplify:

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

Possible Answers:

None of these answers are correct.

$1+2\sin^2x$

$1-2\cos^2x$

Correct answer:

Explanation:

$\sin^2x+\cos^2x=1$

and

$\sin^2x=1-\cos^2x$

Therefore...

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

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

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

=1+1=2

Report an Error

Example Question #131 : Trigonometric Functions

Find the exact value

$sin\left[2tan^{-1}\left(\frac{3}{4}\right)\right]$ .

Possible Answers:

$\frac{12}{25}$

$\frac{6}{5}$

$\frac{9}{8}$

$\frac{24}{25}$

Correct answer:

$\frac{24}{25}$

Explanation:

By the double angle formula

${\right }sin(2x)=2sin(x)cos(x)$

$sin\left[2tan^{-1}\left(\frac{3}{4}\right)\right]=2sin\left[tan^{-1}\left(\frac{3}{4}\right)\right]cos\left[tan^{-1}\left(\frac{3}{4}\right)\right]$

$=2\left(\frac{3}{5}\right)\left(\frac{4}{5}\right)=\frac{24}{25}$

Report an Error

Example Question #22 : Fundamental Trigonometric Identities

Find the exact value

$sin\left[2tan^{-1}\left(\frac{8}{15}\right)\right]$ .

Possible Answers:

$\frac{16}{289}$

$\frac{16}{17}$

$\frac{240}{289}$

$\frac{120}{289}$

Correct answer:

$\frac{240}{289}$

Explanation:

By the double angle formula

{}sin(2x)=2sin(x)cos(x)

$sin\left[2tan^{-1}\left(\frac{8}{15}\right)\right]=2sin\left[tan^{-1}\left(\frac{8}{15}\right)\right]cos\left[tan^{-1}\left(\frac{8}{15}\right)\right]$

$=2\left(\frac{8}{17}\right)\left(\frac{15}{17}\right)=\frac{240}{289}$

Report an Error

Example Question #23 : Fundamental Trigonometric Identities

Find the exact value

$cos\left[2tan^{-1}\left(\frac{5}{12}\right)\right]$ .

Possible Answers:

$\frac{50}{169}$

$\frac{7}{13}$

$\frac{119}{169}$

$-\frac{119}{169}$

Correct answer:

$\frac{119}{169}$

Explanation:

By the double-angula formula for cosine

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

For this problem

$cos\left[2tan^{-1}\left(\frac{5}{12}\right)\right]=cos^2\left[tan^{-1}\left(\frac{5}{12}\right)\right]-sin^2\left[tan^{-1}\left(\frac{5}{12}\right)\right]$

$=\left(\frac{12}{13}\right)^2-\left(\frac{5}{13}\right)^2=\frac{119}{169}$

Report an Error

Example Question #1502 : Pre Calculus

Find the exact value

$sin\left[2sin^{-1}\left(\frac{12}{37}\right)\right]$ .

Possible Answers:

$\frac{24}{37}$

$\frac{840}{1369}$

$\frac{420}{1369}$

$\frac{840}{37}$

Correct answer:

$\frac{840}{1369}$

Explanation:

By the double-angle formula for the sine function

sin(2x)=2sin(x)cos(x)

we have

$x=sin^{-1}\left( \frac{12}{37}\right)$

thus the double angle formula becomes,

$sin\left[2sin^{-1}\left(\frac{12}{37}\right)\right]=2sin\left[sin^{-1}\left(12/37\right)\right]cos\left[sin^{-1}\left(12/37\right)\right]$

$=2\left(\frac{12}{37}\right)\left(\frac{35}{37}\right)=\frac{840}{1369}$

Report an Error

Example Question #132 : Trigonometric Functions

If $\theta=X$ , which of the following best represents $sin(2\theta)$ ?

Possible Answers:

2sinXcosX

cos^2X-sin^2X

1-cos^2X

sinXcosX

sin^2X

Correct answer:

2sinXcosX

Explanation:

The expression $sin(2\theta)$ is a double angle identity that can also be rewritten as:

$2sin(\theta) cos(\theta)$

Replace the value of theta for $\theta=X$ .

The correct answer is: 2sin(X) cos(X)

Report an Error

Example Question #1504 : Pre Calculus

Which expression is equivalent to $\cos(6x)$ ?

Possible Answers:

$1 - 6 \sin ^ 2 x$

$6 \cos ^ 2 x - 1$

$\cos ^ 2 x - \sin ^ 2 x$

$1- 2 \sin^2 (3x)$

$3 \cos ^ 2 (2x ) - 1$

Correct answer:

$1- 2 \sin^2 (3x)$

Explanation:

The relevant trigonometric identity is:

$\cos (2u) = \cos ^ 2 u - \sin ^ 2 u = 2 \cos ^ 2 u - 1 = 1 - 2 \sin ^ 2 u$

In this case, "u" is since 2*3x = 6x .

The only one that actually follows this is $1- 2 \sin^2 (3x)$

Report an Error

View Pre-Calculus Tutors

Mohammad
Certified Tutor

Jamia Millia Islamia, Master of Science, Physics.

View Pre-Calculus Tutors

Tom
Certified Tutor

University of Wisconsin-Madison, Bachelor of Science, Atmospheric Sciences and Meteorology. Embry-Riddle Aeronautical Univers...

View Pre-Calculus Tutors

Jaahanava
Certified Tutor

University of Windsor, Master's/Graduate, Computer Science .

All Precalculus Resources

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

Popular Subjects

Physics Tutors in San Francisco-Bay Area, Spanish Tutors in Los Angeles, GMAT Tutors in Miami, ISEE Tutors in Boston, SAT Tutors in Philadelphia, MCAT Tutors in Miami, Statistics Tutors in Philadelphia, GRE Tutors in Philadelphia, Calculus Tutors in Los Angeles, Spanish Tutors in Boston

Popular Courses & Classes

ISEE Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Chicago, Spanish Courses & Classes in Philadelphia, ISEE Courses & Classes in New York City, LSAT Courses & Classes in Chicago, SSAT Courses & Classes in Denver, GRE Courses & Classes in Washington DC, ACT Courses & Classes in Atlanta, GRE Courses & Classes in Miami, GMAT Courses & Classes in Atlanta

Popular Test Prep

ACT Test Prep in Denver, SSAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Denver, GRE Test Prep in Denver, GRE Test Prep in Chicago, ISEE Test Prep in Los Angeles, GMAT Test Prep in Atlanta, LSAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in San Diego, ACT 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

Precalculus : Trigonometric Functions

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #131 : Trigonometric Functions

Example Question #132 : Trigonometric Functions

Example Question #133 : Trigonometric Functions

Example Question #134 : Trigonometric Functions

Example Question #131 : Trigonometric Functions

Example Question #22 : Fundamental Trigonometric Identities

Example Question #23 : Fundamental Trigonometric Identities

Example Question #1502 : Pre Calculus

Example Question #132 : Trigonometric Functions

Example Question #1504 : Pre Calculus

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: