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 #171 : Trigonometric Functions

Which of the following trigonometric identities is INCORRECT?

Possible Answers:

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

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

$sec (x) = \frac{1}{cos (x)}$

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

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

Correct answer:

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

Explanation:

Cosine and sine are not reciprocal functions.

$sin (x) = \frac{1}{csc (x)}$ and $cos (x) = \frac{1}{sec (x)}$

Report an Error

Example Question #172 : Trigonometric Functions

Using the trigonometric identities prove whether the following is valid:

$\frac{\csc^{2}A}{\sec^{2}A} = \cot^{2}A$

Possible Answers:

Uncertain

True

False

Only in the range of: $0< A < \frac{\pi}{2}$

Only in the range of: $0 < A < 2\pi$

Correct answer:

True

Explanation:

We begin with the left-hand side of the equation and utilize basic trigonometric identities, beginning with converting the inverse functions to their corresponding base functions:

$\frac{\frac{1}{\sin^{2}A}}{\frac{1}{\cos^{2}A}} = \cot^{2}A$

Next, we rewrite the fractional division in order to simplify the equation:

$\frac{1}{\sin^{2}A}\div\frac{1}{\cos^{2}A} = \cot^{2}A$

In fractional division we multiply by the reciprocal as follows:

$\frac{1}{\sin^{2}A}\times \cos^{2}A = \cot^{2}A$

If we reduce the fraction using basic identities we see that the equivalence is proven:

$\frac{\cos^{2}A}{\sin^{2}A} = \cot^{2}A$

$\cot^{2}A = \cot^{2}A$

Report an Error

Example Question #172 : Trigonometric Functions

Which of the following identities is incorrect?

Possible Answers:

$\small \sin(-x)=-\sin(x)$

$\small \sec(-x)=\sec(x)$

$\small \tan(-x)=-\tan(x)$

$\mathrm{cos}(-x)=-\mathrm{cos}(x)$

$\small \csc(-x)=-\csc(x)$

Correct answer:

$\mathrm{cos}(-x)=-\mathrm{cos}(x)$

Explanation:

The true identity is $\small \cos(-x)=\cos(x)$ because cosine is an even function.

Report an Error

Example Question #173 : Trigonometric Functions

State $\tan x$ in terms of sine and cosine.

Possible Answers:

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

$\sin x \cos x$

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

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

$1+\sin x$

Correct answer:

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

Explanation:

The definition of tangent is sine divided by cosine.

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

Report an Error

Example Question #175 : Trigonometric Functions

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

Possible Answers:

$\tan^2 x$

$-\sin x\cos x$

$\sin^2 x$

$-\tan^2 x$

$-\sin^2 x$

Correct answer:

$\sin^2 x$

Explanation:

Using these basic identities:

$\sin(-x)=-\sin x$

$\cos(-x)=\cos(x)$

$\tan(-x)=-\tan x$

we find the original expression to be

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

which simplifies to

$\sin x\cos x\tan x$ .

Further simplifying:

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

The cosines cancel, giving us

$\sin ^2 x$

Report an Error

Example Question #176 : Trigonometric Functions

Which of the following is the best answer for $cos^2(\theta)$ ?

Possible Answers:

$-sin^2(\theta)$

$-sec^2(\theta)$

$tan^2(\theta)-1$

$1-sin^2(\theta)$

$-cot^2(\theta)$

Correct answer:

$1-sin^2(\theta)$

Explanation:

Write the Pythagorean identity.

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

Substract $sin^2(\theta)$ from both sides.

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

The other answers are incorrect.

Report an Error

Example Question #174 : Trigonometric Functions

Express $\frac{1}{\sec x \csc x \tan x}$ in terms of only sines and cosines.

Possible Answers:

$\sin^2x$

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

$\cos x \sin^2 x$

$\sin x \cos^2 x$

$\cos^2 x$

Correct answer:

$\cos^2 x$

Explanation:

The correct answer is $\cos^2 x$ . Begin by substituting $\frac{1}{\sec x}=\cos x$ , $\frac{1}{\csc x}=\sin x$ , and $\frac{1}{\tan x}=\frac{\cos x}{\sin x}$ . This gives us:

$\frac{1}{\sec x\csc x\tan x}=\frac{\cos x\sin x\cos x}{\sin x}=\cos^2 x$ .

Report an Error

Example Question #175 : Trigonometric Functions

Express $\sec x\tan x+\frac{\cot x}{\csc x}$ in terms of only sines and cosines.

Possible Answers:

$\frac{\sin x}{\cos^2 x}+\cos x\sin^2 x$

$\cos x +1$

$\frac{\sin x}{\cos^2 x}+\frac{\cos x}{\sin^2 x}$

$\sin x +1$

$\frac{\sin x}{\cos^2 x}+\cos x$

Correct answer:

$\frac{\sin x}{\cos^2 x}+\cos x$

Explanation:

To solve this problem, use the identities $\sec x =\frac{1}{\cos x}$ , $\tan x=\frac{\sin x}{\cos x}$ , $\cot x =\frac{\cos x}{\sin x}$ , and $\frac{1}{\csc x}=\sin x$ . Then we get

$\sec x\tan x+\frac{\cot x}{\csc x}$

$=\frac{1}{\cos x}\cdot \frac{\sin x}{\cos x}+\sin x\cdot \frac{\cos x}{\sin x}$

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

Report an Error

View Pre-Calculus Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

View Pre-Calculus Tutors

Shivansh
Certified Tutor

University of British Columbia, Bachelor, Math major and data science minor .

View Pre-Calculus Tutors

Andrew
Certified Tutor

University of Wisconsin-Stevens Point, Bachelor of Science, Mathematics. University of Wisconsin-Oshkosh, Master of Science, ...

All Precalculus Resources

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

Popular Subjects

French Tutors in Houston, Computer Science Tutors in Seattle, Statistics Tutors in San Diego, Statistics Tutors in San Francisco-Bay Area, GRE Tutors in Los Angeles, Spanish Tutors in Seattle, Statistics Tutors in Atlanta, LSAT Tutors in New York City, Chemistry Tutors in Chicago, Statistics Tutors in Denver

Popular Courses & Classes

Spanish Courses & Classes in Seattle, GRE Courses & Classes in New York City, SSAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Seattle, LSAT Courses & Classes in Seattle, MCAT Courses & Classes in San Diego, MCAT Courses & Classes in Boston, Spanish Courses & Classes in Phoenix, ACT Courses & Classes in Houston, GRE Courses & Classes in Boston

Popular Test Prep

GRE Test Prep in Houston, SAT Test Prep in Chicago, GRE Test Prep in Philadelphia, ISEE Test Prep in Washington DC, LSAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Miami, ACT Test Prep in Houston, LSAT Test Prep in Denver, SAT Test Prep in Houston, SAT 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 Functions

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #171 : Trigonometric Functions

Example Question #172 : Trigonometric Functions

Example Question #172 : Trigonometric Functions

Example Question #173 : Trigonometric Functions

Example Question #175 : Trigonometric Functions

Example Question #176 : Trigonometric Functions

Example Question #174 : Trigonometric Functions

Example Question #175 : Trigonometric Functions

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: