We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Trigonometry : Unit Circle

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 : Unit Circle

What point corresponds to the angle $-\pi$ on the unit circle?

Possible Answers:

(1,1)

(-1,-1)

(-1,0)

(0,0)

(1,0)

Correct answer:

(-1,0)

Explanation:

The unit circle is the circle of radius one centered at the origin (0,0) in the Cartesian coordinate system. $-\pi$ is equivalent to $-180^{\circ}$ which corresponds to the point (-1,0) on the unit circle.

Report an Error

Example Question #1 : Unit Circle

What point corresponds to an angle of $\frac{5\pi}{2}$ radians on the unit circle?

Possible Answers:

(-1,1)

(1,1)

(0,1)

(0,0)

(-1,-1)

Correct answer:

(0,1)

Explanation:

The unit circle is the circle of radius one centered at the origin (0,0) in the Cartesian coordinate system. $\frac{5\pi}{2}$ radians is equivalent to $\frac{5\pi}{2}\times \frac{180^{\circ}}{\pi}=450^{\circ}$ . This is a full circle $360^{\circ}$ plus a quarter-turn $90^{\circ}$ more. So, the angle $\frac{5\pi}{2}$ corresponds to the point (0,1) on the unit circle.

Report an Error

Example Question #1 : Unit Circle

Give the angle between $0^{\circ}$ and $360^{\circ}$ that corresponds to the point (-1,0) .

Possible Answers:

$180^{\circ}$

$120^{\circ}$

$45^{\circ}$

$60^{\circ}$

$90^{\circ}$

Correct answer:

$180^{\circ}$

Explanation:

The angle $\pi$ or $180^{\circ}$ corresponds to the point (-1,0) .

Report an Error

Example Question #3 : Unit Circle

What point corresponds to the angle $\frac{\pi}{2}$ on the unit circle?

Possible Answers:

(-1,-1)

(1,1)

(0,1)

(1,0)

(0,-1)

Correct answer:

(0,1)

Explanation:

The unit circle is the circle of radius one centered at the origin (0,0) in the Cartesian coordinate system. $\frac{\pi}{2}$ is equivalent to $90^{\circ}$ which corresponds to the point (0,1) on the unit circle.

Report an Error

Example Question #2 : Unit Circle

Which of the following points is NOT on the unit circle?

Possible Answers:

(1,0)

(0, -1)

$(-\frac{1}{2}, -\frac{\sqrt{3}}{2})$

$(\frac{-\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$

$(\frac{\sqrt{3}}{2}, \frac{\sqrt{2}}{2})$

Correct answer:

$(\frac{\sqrt{3}}{2}, \frac{\sqrt{2}}{2})$

Explanation:

For a point to be on the unit circle, it has to have a radius of one. Therefore, the sum of the squares of point's coordinates must also equal one.

Let's try the point $(\frac{\sqrt{3}}{2}, \frac{\sqrt{2}}{2})$ .

$(\frac{\sqrt{3}}{2})^{2} + (\frac{\sqrt{2}}{2})^{2} = \frac{5}{4} \neq 1$

Therefore, this point is not on the unit circle.

Report an Error

Example Question #3 : Unit Circle

When looking at the unit circle, what are the coordinates for an angle of $\frac{\pi}{4}$ ?

Possible Answers:

$\left(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)$

$\left(\frac{\sqrt{3}}{2},\frac{1}{2}\right)$

$(\sqrt{2},\sqrt{2})$

$\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)$

(0,1)

Correct answer:

$\left(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)$

Explanation:

The coordinates of the point on the circle for each angle are $(\cos\theta,\sin\theta)$ .

Since $\cos\frac{\pi}{4}=\frac{\sqrt{2}}{2}$ and $\sin\frac{\pi}{4}=\frac{\sqrt{2}}{2}$ , the point will be $(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$ .

Report an Error

Example Question #1 : Unit Circle

What is the radius of the unit circle?

Possible Answers:

$\frac{3}{4}$

$\frac{1}{2}$

Correct answer:

Explanation:

By definition, the radius of the unit circle is 1.

Report an Error

Example Question #1 : Unit Circle

What point corresponds to the angle $\frac{\pi}{3}$ on the unit circle?

Possible Answers:

$\left(\frac{1}{2},\frac{1}{2}\right)$

(0,-1)

$\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)$

$\left(\frac{\sqrt{3}}{2},\frac{1}{2}\right)$

(1,1)

Correct answer:

$\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)$

Explanation:

In order to find the point corresponds to the angle $\frac{\pi}{3}$ on the unit circle we can write:

$t=\frac{\pi}{3}\ or\ 60^{\circ}$

In the unit circle which has the radious of R=1 we can write:

$cos\ t=\frac{x}{R}=\frac{x}{1}=x\Rightarrow x=cos(60^{\circ})=\frac{1}{2}$

$sin\ t=\frac{y}{R}=\frac{y}{1}=y\Rightarrow y=sin(60^{\circ})=\frac{\sqrt{3}}{2}$

So the point corresponds to the angle $\frac{\pi}{3}$ on the unit circle is $(\frac{1}{2},\frac{\sqrt{3}}{2})$

Report an Error

Example Question #1 : Unit Circle

What point corresponds to an angle of $540^{\circ}$ on the unit circle?

Possible Answers:

(0,1)

(-1,-1)

(-1,0)

(1,-1)

(1,1)

Correct answer:

(-1,0)

Explanation:

The unit circle is the circle of radius one centered at the origin (0,0) in the Cartesian coordinate system. $540^{\circ}$ is a full circle $360^{\circ}$ plus a $180^{\circ}$ more. So, the angle $540^{\circ}$ corresponds to the point (-1,0) on the unit circle.

Report an Error

Example Question #1 : Unit Circle

What must be the area of the unit circle?

Possible Answers:

$2\pi$

$\frac{\pi}{4}$

$\frac{\pi}{2}$

The area can vary.

$\pi$

Correct answer:

$\pi$

Explanation:

The unit circle must have a radius of 1.

Use the circular area formula to find the area.

$A_{circle}= \pi r^2= \pi$

Report an Error

View Trigonometry Tutors

Vicky
Certified Tutor

Clemson University, Doctor of Science, Civil Engineering.

View Trigonometry Tutors

Vandana
Certified Tutor

Jawaharlal Nehru Technological University, Bachelor of Technology, Civil Engineering. Florida International University, Maste...

View Trigonometry Tutors

Crystal
Certified Tutor

SUNY at Binghamton, Bachelor of Science, Mechanical Engineering.

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

Spanish Courses & Classes in Atlanta, GMAT Courses & Classes in Miami, Spanish Courses & Classes in Washington DC, GRE Courses & Classes in Los Angeles, ISEE Courses & Classes in Houston, ACT Courses & Classes in Philadelphia, LSAT Courses & Classes in Phoenix, MCAT Courses & Classes in Seattle, ACT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

ACT Test Prep in Seattle, GMAT Test Prep in Philadelphia, SAT Test Prep in New York City, GRE Test Prep in Dallas Fort Worth, ACT Test Prep in Dallas Fort Worth, MCAT Test Prep in Seattle, SAT Test Prep in Miami, GMAT Test Prep in New York City, LSAT Test Prep in Phoenix, SSAT Test Prep in Denver

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 : Unit Circle

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #1 : Unit Circle

Example Question #1 : Unit Circle

Example Question #1 : Unit Circle

Example Question #3 : Unit Circle

Example Question #2 : Unit Circle

Example Question #3 : Unit Circle

Example Question #1 : Unit Circle

Example Question #1 : Unit Circle

Example Question #1 : Unit Circle

Example Question #1 : Unit Circle

All Trigonometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: