Call Now to Set Up Tutoring:

(888) 888-0446

Trigonometry : Trigonometry

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 #13 : Angles In Different Quadrants

Which two angles are both in the same quadrant?

Possible Answers:

$\small \frac{13\pi}{4}$ and $\small \frac{-\pi}{6}$

$\small \frac{-4\pi}{3}$ and $\small \frac{9\pi}{4}$

$\small \frac{-2\pi}{3}$ and $\small \frac{13\pi}{4}$

$\small \small \frac{11\pi}{6}$ and $\small \frac{\pi}{4}$

$\small \frac{-2\pi}{3}$ and $\frac{-4\pi}{3}$

Correct answer:

$\small \frac{-2\pi}{3}$ and $\small \frac{13\pi}{4}$

Explanation:

First lets identify the different quadrants.

Quadrant I: $0\rightarrow \frac{\pi}{2}$

Quadrant II: $\frac{\pi}{2}\rightarrow \pi$

Quadrant III: $\pi \rightarrow \frac{3\pi}{2}$

Quadrant IV: $\frac{3\pi}{2}\rightarrow 2\pi$

Now looking at our possible answer choices, we will add or subtract $2\pi$ until we get the reduced fraction of the angle. This will tell us which quadrant the angle lies in.

$\small \frac{-2\pi}{3}+2\pi=\frac{-2\pi}{3}+\frac{6\pi}{3}=\frac{4\pi}{3}$ thus in quadrant III.

$\small \frac{13\pi}{4}-2\pi=\frac{13\pi}{4}-\frac{8\pi}{4}=\frac{5\pi}{4}$ thus in quadrant III.

Therefore,

$\small \frac{-2\pi}{3}$ and $\small \frac{13\pi}{4}$ is the correct answer.

Report an Error

Example Question #72 : Angles

Which angle is in quadrant II?

Possible Answers:

$\small \frac{-4\pi}{3}$

$\small \frac{-5\pi}{3}$

$\small \frac{-\pi}{4}$

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

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

Correct answer:

$\small \frac{-4\pi}{3}$

Explanation:

First lets identify the different quadrants.

Quadrant I: $0\rightarrow \frac{\pi}{2}$

Quadrant II: $\frac{\pi}{2}\rightarrow \pi$

Quadrant III: $\pi \rightarrow \frac{3\pi}{2}$

Quadrant IV: $\frac{3\pi}{2}\rightarrow 2\pi$

The correct answer, $\small \frac{-4\pi}{3}$ , is coterminal with $\small \frac{2\pi}{3}$ .

We can figure this out by adding $\small 2\pi$ , or equivalently $\small \frac{6\pi}{3}$ to get $\small \frac{2\pi}{3}$ , or we can count thirds of pi around the unit circle clockwise. Either way, it is the only angle that ends in the second quadrant.

Report an Error

Example Question #11 : Angles In Different Quadrants

In which angle would a 50000^o angle terminate in?

Possible Answers:

Quadrant IV

Quadrant II

Quadrant I

Between quadrants

Quadrant III

Correct answer:

Quadrant IV

Explanation:

One way to uncover which quadrant this angle lies is to ask how many complete revolutions this angle makes by dividing it by 360 (and rounding down to the nearest whole number).

With a calculator we find that 50000^o makes 138 full revolutions. Now the key lies in what the remainder the angle makes with 138 revolutions:

50000^o - 138 * 360^o = 320^o

270^o < 320^o < 360^o , therefore our angle lies in the fourth quadrant.

Alternatively, we could find evaluate $sin \ 50000^o$ and $cos \ 50000^o$ .

The former (sine) gives us a negative number whereas the latter (cosine) gives a positive. The only quadrant in which sine is negative and cosine is positive is the fourth quadrant.

Report an Error

Example Question #12 : Angles In Different Quadrants

Which quadrant does $135^\circ$ belong?

Possible Answers:

III

Correct answer:

Explanation:

Step 1: Define the quadrants and the angles that go in:

QI:

$0^\circ<x\leq 90^\circ$

QII:

$90^\circ < x \leq 180^\circ$

QIII:

$180^\circ < x \leq 270^\circ$

QIV:

$270^\circ < x \leq 360$

Step 2: Find the quadrant where $135^\circ$ is:

The angle is located in QII (Quadrant II)

Report an Error

Example Question #13 : Angles In Different Quadrants

The angle $\theta=17\pi/4$ is in which quadrant?

Possible Answers:

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

Correct answer:

Quadrant I

Explanation:

First, using the unit circle, we can see that the denominator has a four in it, which means it is a multiple of $\pi/4$ .

We want to reduce the angle down until we can visualize which quadrant it is in. You can subtract $2\pi$ away from the angle each time (because that is just one revolution, and we end up at the same spot).

If you subtract away $2\pi$ twice, you are left with $\pi/4$ , which is in quadrant I.

$17\pi/4-8\pi/4-8\pi/4=\pi/4$ .

Report an Error

Example Question #11 : Angles In Different Quadrants

Which of the following angles lies in the second quadrant?

Possible Answers:

$\frac{11\pi }{6}$

$\frac{\pi }{3}$

$\frac{7\pi }{2}$

$\frac{4\pi }{3}$

$\frac{11\pi }{4}$

Correct answer:

$\frac{11\pi }{4}$

Explanation:

The second quadrant contains angles between $\frac{\pi }{2}$ and $\pi$ , plus those with additional multiples of $2\pi$ . The angle $\frac{11\pi }{4}$ is, after subtracting $2\pi$ , is simply $\frac{3\pi }{4}$ , which puts it in the second quadrant.

Report an Error

Example Question #1 : Sin, Cos, Tan

Find the value of the trigonometric function in fraction form for triangle ABC .

Triangle

What is the cosine of $\angle B$ ?

Possible Answers:

7/24

24/25

$\frac{7}{25}$

Correct answer:

$\frac{7}{25}$

Explanation:

The cosine of an angle is the value of the adjacent side over the hypotenuse.

Therefore:

$cos \angle B = \frac{adjacent}{hypotenuse} = \frac{7}{25}$

Report an Error

Example Question #1 : Sin, Cos, Tan

What is the value of sin(30)+sin(60) ?

Possible Answers:

$\frac{\sqrt3+1}{2}$

$\frac{\sqrt3-1}{2}$

Correct answer:

$\frac{\sqrt3+1}{2}$

Explanation:

Solve each term separately.

$cos(30)= \frac{\sqrt3}{2}$

$cos(60)=\frac{1}{2}$

Add both terms.

$\frac{\sqrt3}{2}+\frac{1}{2}= \frac{\sqrt3+1}{2}$

Report an Error

Example Question #3 : Sin, Cos, Tan

Determine the value of 2tan(120) .

Possible Answers:

$-2\sqrt3$

$-\frac{\sqrt3}{2}$

$2\sqrt3$

$\sqrt3$

$-\sqrt3$

Correct answer:

$-2\sqrt3$

Explanation:

Rewrite 2tan(120) in terms of sines and cosines.

$2tan(120)=2(\frac{sin(120)}{cos(120)})=2(\frac{\frac{\sqrt3}{2}}{-\frac{1}{2}})$

Simplify the complex fraction.

$2(\frac{\frac{\sqrt3}{2}}{-\frac{1}{2}})= 2\times\frac{\sqrt3}{2}\times-2 = -2\sqrt3$

Report an Error

Example Question #1 : Sin, Cos, Tan

Find the value of $\frac{1}{2}sin(45)+ tan(60)$ .

Possible Answers:

$\frac{\sqrt2-4\sqrt3}{2}$

$\sqrt2+\sqrt3$

$\frac{3\sqrt2+\sqrt3}{12}$

$\frac{\sqrt2+4\sqrt3}{2}$

$\frac{\sqrt2+4\sqrt3}{4}$

Correct answer:

$\frac{\sqrt2+4\sqrt3}{4}$

Explanation:

To find the value of $\frac{1}{2}sin(45)+ tan(60)$ , solve each term separately.

$\frac{1}{2}sin(45)=\frac{1}{2} \cdot \frac{\sqrt2}{2} = \frac{\sqrt2}{4}$

$tan(60) = \sqrt3$

Sum the two terms.

$\frac{\sqrt2}{4}+\sqrt3 = \frac{\sqrt2}{4}+\frac{4\sqrt3}{4} = \frac{\sqrt2+4\sqrt3}{4}$

Report an Error

View Trigonometry Tutors

Michael
Certified Tutor

University of Richmond, Bachelor of Science, Mathematics. Central Connecticut State University, Master of Arts, Mathematics.

View Trigonometry Tutors

James
Certified Tutor

Georgia Institute of Technology-Main Campus, Current Undergrad Student, Computer Science.

View Trigonometry Tutors

Rodolfo
Certified Tutor

The University of Texas at San Antonio, 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

Spanish Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Miami, ACT Courses & Classes in Los Angeles, GMAT Courses & Classes in Los Angeles, ACT Courses & Classes in Houston, LSAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Philadelphia, ISEE Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in San Diego, ISEE Courses & Classes in Phoenix

Popular Test Prep

GMAT Test Prep in Washington DC, GMAT Test Prep in Denver, GMAT Test Prep in Boston, GMAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Dallas Fort Worth, ISEE Test Prep in New York City, SSAT Test Prep in Philadelphia, GMAT Test Prep in Los Angeles, GRE Test Prep in Boston, GRE Test Prep in Houston

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 : Trigonometry

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #13 : Angles In Different Quadrants

Example Question #72 : Angles

Example Question #11 : Angles In Different Quadrants

Example Question #12 : Angles In Different Quadrants

Example Question #13 : Angles In Different Quadrants

Example Question #11 : Angles In Different Quadrants

Example Question #1 : Sin, Cos, Tan

Example Question #1 : Sin, Cos, Tan

Example Question #3 : Sin, Cos, Tan

Example Question #1 : Sin, Cos, Tan

All Trigonometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: