Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Trigonometry

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

Example Question #3 : The Unit Circle And Radians

What is $\sin(\frac{3\pi}{4})$ $\displaystyle \sin(\frac{3\pi}{4})$?

Possible Answers:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\displaystyle 1$

$\frac{-\sqrt2}{2}$ $\displaystyle \frac{-\sqrt2}{2}$

$\displaystyle -1$

$\frac{\sqrt{2}}{2}$ $\displaystyle \frac{\sqrt{2}}{2}$

Correct answer:

$\frac{\sqrt{2}}{2}$ $\displaystyle \frac{\sqrt{2}}{2}$

Explanation:

Using the unit circle, $\sin(\frac{3\pi}{4})=\frac{\sqrt2}{2 }$ $\displaystyle \sin(\frac{3\pi}{4})=\frac{\sqrt2}{2 }$. You can also think of this as the sine of $135^\circ$ $\displaystyle 135^\circ$, which would also be $\frac{\sqrt2}{2}$ $\displaystyle \frac{\sqrt2}{2}$.

Report an Error

Example Question #4 : The Unit Circle And Radians

What is $\cos (\frac{3\pi}{4})$ $\displaystyle \cos (\frac{3\pi}{4})$?

Possible Answers:

$\displaystyle 1$

$\displaystyle -1$

$\frac{2\sqrt2}{2}$ $\displaystyle \frac{2\sqrt2}{2}$

$\frac{\sqrt2}{2}$ $\displaystyle \frac{\sqrt2}{2}$

$-\frac{\sqrt2}{2}$ $\displaystyle -\frac{\sqrt2}{2}$

Correct answer:

$-\frac{\sqrt2}{2}$ $\displaystyle -\frac{\sqrt2}{2}$

Explanation:

Using the unit circle, you can see that the $\cos (\frac{3\pi}{4})=-\frac{\sqrt2}{2}$ $\displaystyle \cos (\frac{3\pi}{4})=-\frac{\sqrt2}{2}$. Since the angle is in Qudrant II, sine is positive and cosine is negative.

Report an Error

Example Question #5 : The Unit Circle And Radians

What is $\sin(\frac{\pi}{4})$ $\displaystyle \sin(\frac{\pi}{4})$?

Possible Answers:

$\frac{\sqrt2}{2}$ $\displaystyle \frac{\sqrt2}{2}$

$\displaystyle -1$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$-\frac{\sqrt2}{2}$ $\displaystyle -\frac{\sqrt2}{2}$

$\displaystyle 1$

Correct answer:

$\frac{\sqrt2}{2}$ $\displaystyle \frac{\sqrt2}{2}$

Explanation:

Using the unit circle, $\sin(\frac{\pi}{4})=\frac{\sqrt2}{2 }$ $\displaystyle \sin(\frac{\pi}{4})=\frac{\sqrt2}{2 }$. You can also think of this as the sine of $45^\circ$ $\displaystyle 45^\circ$, which would also be $\frac{\sqrt2}{2}$ $\displaystyle \frac{\sqrt2}{2}$.

Report an Error

Example Question #1 : The Unit Circle And Radians

What is $\sin(\pi)$ $\displaystyle \sin(\pi)$?

Possible Answers:

$\frac{\sqrt{2}}{2}$ $\displaystyle \frac{\sqrt{2}}{2}$

$\frac{\sqrt{3}}{2}$ $\displaystyle \frac{\sqrt{3}}{2}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\displaystyle 1$

$\displaystyle 0$

Correct answer:

$\displaystyle 0$

Explanation:

If you examine the unit circle, you'll see that that $\sin(\pi)=0$ $\displaystyle \sin(\pi)=0$.

Report an Error

Example Question #2 : The Unit Circle And Radians

What is $\cos(\pi)$ $\displaystyle \cos(\pi)$?

Possible Answers:

$\displaystyle 0$

$\displaystyle -1$

$\frac{\sqrt2}{2}$ $\displaystyle \frac{\sqrt2}{2}$

$\frac{\sqrt3}{2}$ $\displaystyle \frac{\sqrt3}{2}$

$\displaystyle 1$

Correct answer:

$\displaystyle -1$

Explanation:

If you examine the unit circle, you'll see that the value of $\cos(\pi)=-1$ $\displaystyle \cos(\pi)=-1$. You can also get this by examining a cosine graph and you'll see it crosses the point $(\pi,-1)$ $\displaystyle (\pi,-1)$.

Report an Error

Example Question #11 : The Unit Circle And Radians

What is the value of the angle $\frac{3\pi}{2}$ $\displaystyle \frac{3\pi}{2}$ radians when converted to degrees?

Possible Answers:

270 $\displaystyle 270$

$\displaystyle 90$

$\displaystyle -45$

135 $\displaystyle 135$

$\displaystyle -180$

Correct answer:

270 $\displaystyle 270$

Explanation:

The answer can be found using the conversion of 1 radian equals $\frac{180}{\pi}$ $\displaystyle \frac{180}{\pi}$ degrees. Multiplying $\frac{3\pi}{2}$ $\displaystyle \frac{3\pi}{2}$ by this conversion factor gives 270 degrees.

Report an Error

Example Question #2 : Understanding Radians And Conversions

A point has Cartesian coordinates (1,3) $\displaystyle (1,3)$. Rewrite this as an ordered pair in the polar coordinate plane, rounding the coordinates to the nearest hundredth.

Possible Answers:

$\displaystyle (3.16,0.80)$

$\displaystyle (2.83, 1.25)$

$\displaystyle (3.16,0.32)$

$\displaystyle (3.16,1.25)$

$\displaystyle (2.83, 0.32)$

Correct answer:

$\displaystyle (3.16,1.25)$

Explanation:

Set $\displaystyle x=1, y=3$. Calculate the polar coordinates $(r,\theta )$ $\displaystyle (r,\theta )$ as follows:

$r = \sqrt{x^{2}+y^{2}}= \sqrt{1^{2}+3^{2}}=\sqrt{10} \approx 3.16$ $\displaystyle r = \sqrt{x^{2}+y^{2}}= \sqrt{1^{2}+3^{2}}=\sqrt{10} \approx 3.16$

$\theta = \arctan \frac{y}{x}= \arctan \frac{3}{1} = \arctan 3 \approx 1.25$ $\displaystyle \theta = \arctan \frac{y}{x}= \arctan \frac{3}{1} = \arctan 3 \approx 1.25$

Report an Error

Example Question #3 : Understanding Radians And Conversions

How many degrees are in $\frac{\pi}{6}$ $\displaystyle \frac{\pi}{6}$ radians?

Possible Answers:

$60^\circ$ $\displaystyle 60^\circ$

$120^\circ$ $\displaystyle 120^\circ$

$45^\circ$ $\displaystyle 45^\circ$

$360^\circ$ $\displaystyle 360^\circ$

$30^\circ$ $\displaystyle 30^\circ$

Correct answer:

$30^\circ$ $\displaystyle 30^\circ$

Explanation:

$\frac{x^\circ}{\frac{\pi}{6}}=\frac{180^\circ}{\pi}$ $\displaystyle \frac{x^\circ}{\frac{\pi}{6}}=\frac{180^\circ}{\pi}$

Cross multiply:

$x^\circ*\pi=180^\circ*\frac{\pi}{6}$ $\displaystyle x^\circ*\pi=180^\circ*\frac{\pi}{6}$

Notice that the $\pi$ $\displaystyle \pi$'s cancel out:

$x^\circ=180^\circ*\frac{1}{6}$ $\displaystyle x^\circ=180^\circ*\frac{1}{6}$

$x^\circ=30^\circ$ $\displaystyle x^\circ=30^\circ$

Report an Error

Example Question #12 : The Unit Circle And Radians

How many radians are in $180^\circ$ $\displaystyle 180^\circ$?

Possible Answers:

$\frac{\pi}{2}$ $\displaystyle \frac{\pi}{2}$

$3\pi$ $\displaystyle 3\pi$

$\pi$ $\displaystyle \pi$

$2\pi$ $\displaystyle 2\pi$

$4\pi$ $\displaystyle 4\pi$

Correct answer:

$\pi$ $\displaystyle \pi$

Explanation:

The relationship between degrees and radians is $180^\circ=\pi$ $\displaystyle 180^\circ=\pi$ radians. Therefore, $180^\circ$ $\displaystyle 180^\circ$ would be $\pi$ $\displaystyle \pi$ radians.

Report an Error

Example Question #1 : Understanding Radians And Conversions

Express in radians: $125^{\circ }$ $\displaystyle 125^{\circ }$

Possible Answers:

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

$\frac{5\pi }{9}$ $\displaystyle \frac{5\pi }{9}$

$\frac{15\pi }{36}$ $\displaystyle \frac{15\pi }{36}$

$\frac{11\pi }{18}$ $\displaystyle \frac{11\pi }{18}$

$\frac{25\pi }{36}$ $\displaystyle \frac{25\pi }{36}$

Correct answer:

$\frac{25\pi }{36}$ $\displaystyle \frac{25\pi }{36}$

Explanation:

Since $180 ^{\circ } = \pi \textrm{ rad}$ $\displaystyle 180 ^{\circ } = \pi \textrm{ rad}$, we can convert as follows:

$125 \cdot \frac{\pi }{180} = \frac{25\pi }{36}$ $\displaystyle 125 \cdot \frac{\pi }{180} = \frac{25\pi }{36}$

Report an Error

View Tutors

Yosef
Certified Tutor

New York University, Masters in Business Administration, Business Administration and Management.

View Tutors

Connie
Certified Tutor

United States Institute of Language & Clerical Studies, Bachelor of Education, Teaching English as a Second Language (ESL).

View Tutors

Chhavi
Certified Tutor

SUNY at Binghamton, Master of Science, Mathematics.

All High School Math Resources

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

Popular Subjects

Statistics Tutors in Boston, Statistics Tutors in New York City, SAT Tutors in New York City, Biology Tutors in Denver, LSAT Tutors in Philadelphia, ISEE Tutors in San Diego, Reading Tutors in New York City, MCAT Tutors in San Diego, SAT Tutors in Phoenix, Calculus Tutors in Los Angeles

Popular Courses & Classes

GRE Courses & Classes in Houston, GMAT Courses & Classes in Miami, SAT Courses & Classes in Washington DC, Spanish Courses & Classes in Phoenix, GMAT Courses & Classes in San Diego, ACT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in San Diego, SAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Philadelphia, SSAT Courses & Classes in Miami

Popular Test Prep

GRE Test Prep in San Francisco-Bay Area, GRE Test Prep in Seattle, SSAT Test Prep in Denver, LSAT Test Prep in New York City, LSAT Test Prep in Philadelphia, GRE Test Prep in San Diego, SSAT Test Prep in Washington DC, ACT Test Prep in Dallas Fort Worth, GRE Test Prep in Denver, MCAT Test Prep in Seattle

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 : Trigonometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #3 : The Unit Circle And Radians

Example Question #4 : The Unit Circle And Radians

Example Question #5 : The Unit Circle And Radians

Example Question #1 : The Unit Circle And Radians

Example Question #2 : The Unit Circle And Radians

Example Question #11 : The Unit Circle And Radians

Example Question #2 : Understanding Radians And Conversions

Example Question #3 : Understanding Radians And Conversions

Example Question #12 : The Unit Circle And Radians

Example Question #1 : Understanding Radians And Conversions

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: