We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Angles

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 Next →

Example Question #21 : Trigonometry

Find a coterminal angle for $-55^{\circ}$ .

Possible Answers:

$-15^{\circ}$

$305^{\circ}$

$85^{\circ}$

$360^{\circ}$

$300^{\circ}$

Correct answer:

$305^{\circ}$

Explanation:

Coterminal angles are angles that, when drawn in the standard position, share a terminal side. You can find these angles by adding or subtracting 360 to the given angle. Thus, the only angle measurement that works from the answers given is $305^{\circ}$ .

Report an Error

Example Question #2 : Understanding Coterminal Angles

Which of the following angles is coterminal with $\frac{5\pi}{9}$ ?

Possible Answers:

Each angle given in the other choices is coterminal with $\frac{5\pi}{9}$ .

$-\frac{13\pi}{9}$

$-\frac{31\pi}{9}$

$\frac{41\pi}{9}$

$\frac{23\pi}{9}$

Correct answer:

Each angle given in the other choices is coterminal with $\frac{5\pi}{9}$ .

Explanation:

For an angle to be coterminal with $\theta$ , that angle must be of the form $\theta + 2\pi N$ for some integer - or, equivalently, the difference of the angle measures multiplied by $\frac{1}{2\pi}$ must be an integer. We apply this test to all four choices.

$\frac{41\pi}{9}$ :

$\left ( \frac{1}{2\pi } \right ) \left (\frac{41\pi}{9}- \frac{5\pi}{9}\right )$

$=\left ( \frac{1}{2\pi } \right )\left ( \frac{36\pi}{9} \right ) =\left ( \frac{1}{2\pi } \right )4 \pi =2$

$\frac{23\pi}{9}$ :

$\left ( \frac{1}{2\pi } \right ) \left (\frac{23\pi}{9}- \frac{5\pi}{9}\right )$

$=\left ( \frac{1}{2\pi } \right )\left ( \frac{18\pi}{9} \right ) =\left ( \frac{1}{2\pi } \right )2 \pi =1$

$-\frac{13\pi}{9}$ :

$\left ( \frac{1}{2\pi } \right ) \left (-\frac{13\pi}{9}- \frac{5\pi}{9}\right )$

$=\left ( \frac{1}{2\pi } \right )\left ( \frac{-18\pi}{9} \right ) =\left ( \frac{1}{2\pi } \right )\left (- 2 \pi \right )=-1$

$-\frac{31\pi}{9}$ :

$\left ( \frac{1}{2\pi } \right ) \left (-\frac{31\pi}{9}- \frac{5\pi}{9}\right )$

$=\left ( \frac{1}{2\pi } \right )\left ( \frac{-36\pi}{9} \right ) =\left ( \frac{1}{2\pi } \right )\left (- 4 \pi \right )=-2$

All four choices pass the test, so all four angles are coterminal with $\frac{5\pi}{9}$ .

Report an Error

Example Question #4 : Understanding Coterminal Angles

$\textup{Which of the following angle measures, given in radians, is coterminal with an}$

$\textup{an angle of 90 degrees?}$

Possible Answers:

$-\frac{\pi }{2}$

$2\pi$

$\frac{5\pi }{2}$

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

$\pi$

Correct answer:

$\frac{5\pi }{2}$

Explanation:

$90\textup{ degrees }=\frac{\pi }{2}\:\: \textup{ Coterminal angles share the same position on the unit circle.}$

$\textup{Therefore, coterminal angles can be found by adding or subtracting multiples of }2\pi$ .

$\frac{\pi }{2}+2\pi=\frac{5\pi }{2}$

Report an Error

Example Question #5 : Understanding Coterminal Angles

Which of the following choices represents a pair of coterminal angles?

Possible Answers:

$\frac{17\pi }{3} \textrm{ and } \frac{23\pi }{3}$

$\frac{17\pi }{2} \textrm{ and } \frac{23\pi }{2}$

$\frac{17\pi }{4} \textrm{ and } \frac{23\pi }{4}$

$\frac{17\pi }{5} \textrm{ and } \frac{23\pi }{5}$

$\frac{17\pi }{6} \textrm{ and } \frac{23\pi }{6}$

Correct answer:

$\frac{17\pi }{3} \textrm{ and } \frac{23\pi }{3}$

Explanation:

For two angles to be coterminal, they must differ by $2\pi N$ for some integer - or, equivalently, the difference of the angle measures multiplied by $\frac{1}{2\pi}$ must be an integer. We apply this test to all five choices.

$\frac{17\pi }{2} \textrm{ and } \frac{23\pi }{2}$ :

$\frac{1}{2\pi } \cdot \left ( \frac{23\pi }{2} - \frac{17\pi }{2} \right ) = \frac{1}{2\pi } \cdot \frac{6\pi }{2} = \frac{3 }{2}$

$\frac{17\pi }{3} \textrm{ and } \frac{23\pi }{3}$ :

$\frac{1}{2\pi } \cdot \left ( \frac{23\pi }{3} - \frac{17\pi }{3} \right ) = \frac{1}{2\pi } \cdot \frac{6\pi }{3} = 1$

$\frac{17\pi }{4} \textrm{ and } \frac{23\pi }{4}$ :

$\frac{1}{2\pi } \cdot \left ( \frac{23\pi }{4} - \frac{17\pi }{4} \right ) = \frac{1}{2\pi } \cdot \frac{6\pi }{4} = \frac{3 }{4}$

$\frac{17\pi }{5} \textrm{ and } \frac{23\pi }{5}$ :

$\frac{1}{2\pi } \cdot \left ( \frac{23\pi }{5} - \frac{17\pi }{5} \right ) = \frac{1}{2\pi } \cdot \frac{6\pi }{5} = \frac{3 }{5}$

$\frac{17\pi }{6} \textrm{ and } \frac{23\pi }{6}$ :

$\frac{1}{2\pi } \cdot \left ( \frac{23\pi }{6} - \frac{17\pi }{6} \right ) = \frac{1}{2\pi } \cdot \frac{6\pi }{6} = \frac{1 }{2}$

The only angles that pass the test - and are therefore coterminal - are $\frac{17\pi }{3} \textrm{ and } \frac{23\pi }{3}$ .

Report an Error

Example Question #81 : Pre Calculus

Which one of these is positive in quadrant III?

Possible Answers:

No trig functions

Sine

Tangent

All trig functions

Cosine

Correct answer:

Tangent

Explanation:

The pattern for positive functions is All Student Take Calculus. In quandrant I, all trigonometric functions are positive. In quadrant II, sine is positive. In qudrant III, tangent is positive. In quadrant IV, cosine is positive.

Report an Error

← Previous 1 2 Next →

View Tutors

Heather
Certified Tutor

University of Wisconsin-River Falls, Bachelor of Science, Mathematics. University of Iowa, Master of Science, Mathematics.

View Tutors

David
Certified Tutor

University of Toronto, Bachelor in Arts, Philosophy.

View Tutors

Jaroslaw
Certified Tutor

Heriot Watt University, Master of Science, Physics. Heriot Watt University, Doctor of Science, Theoretical and Mathematical P...

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

MCAT Tutors in Atlanta, Calculus Tutors in Miami, Physics Tutors in Washington DC, Statistics Tutors in San Diego, Algebra Tutors in Houston, MCAT Tutors in Houston, Physics Tutors in Chicago, GRE Tutors in Washington DC, Statistics Tutors in Washington DC, Computer Science Tutors in Phoenix

Popular Courses & Classes

LSAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in New York City, GMAT Courses & Classes in Chicago, ACT Courses & Classes in Washington DC, SSAT Courses & Classes in Denver, GMAT Courses & Classes in Denver, LSAT Courses & Classes in Washington DC, GRE Courses & Classes in Houston, MCAT Courses & Classes in New York City, SSAT Courses & Classes in Seattle

Popular Test Prep

ISEE Test Prep in San Diego, MCAT Test Prep in Chicago, MCAT Test Prep in Seattle, GMAT Test Prep in Chicago, GMAT Test Prep in San Diego, SAT Test Prep in Washington DC, GMAT Test Prep in San Francisco-Bay Area, SAT Test Prep in San Francisco-Bay Area, GRE Test Prep in Houston, GRE Test Prep in Chicago

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

High School Math : Angles

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #21 : Trigonometry

Example Question #2 : Understanding Coterminal Angles

Example Question #4 : Understanding Coterminal Angles

Example Question #5 : Understanding Coterminal Angles

Example Question #81 : Pre Calculus

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: