We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Trigonometry : Sin, Cos, Tan

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 : Trigonometry

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

Triangle

What is the cosine of $\angle B$ ?

Possible Answers:

24/25

7/24

$\frac{7}{25}$

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 #1 : Sin, Cos, Tan

Determine the value of 2tan(120) .

Possible Answers:

$\sqrt3$

$-\sqrt3$

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

$-2\sqrt3$

$2\sqrt3$

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 #2 : Sin, Cos, Tan

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

Possible Answers:

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

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

$\sqrt2+\sqrt3$

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

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

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

Example Question #2 : Sine, Cosine, & Tangent

Select the ratio that would give Tan B.

Possible Answers:

None of the other answers.

$\tan B=\frac{AC}{AB}$

$\tan B=\frac{CB}{AB}$

$\tan B=\frac{AB}{AC}$

$\tan B=\frac{CB}{AC}$

Correct answer:

$\tan B=\frac{AC}{AB}$

Explanation:

We need the Tan B. Which side lengths correspond to this ratio?

$\tan=\frac{opp}{adj}$

Report an Error

Example Question #4 : Sin, Cos, Tan

Calculate $tan(\frac{4\pi}{3})$ .

Possible Answers:

$-\sqrt{3}$

$\sqrt{3}$

Correct answer:

$\sqrt{3}$

Explanation:

The tangent function has a period of $\pi$ units. That is,

$tan(x+n\pi)=tanx$

for all $n\in\mathbb{Z}$ .

Since $\frac{4\pi}{3}=\frac{\pi}{3}+\pi$ , we can rewrite the original expression $tan(\frac{4\pi}{3})$ as follows:

$tan(\frac{4\pi}{3})=tan(\frac{\pi}{3}+\pi)$

$=tan(\frac{\pi}{3})$

$=\frac{sin(\frac{\pi}{3})}{cos(\frac{\pi}{3})}$

$=\frac{(\frac{\sqrt{3}}{2})}{(\frac{1}{2})}$

$=\sqrt{3}$

Hence,

$tan(\frac{4\pi}{3})=\sqrt{3}$

Report an Error

Example Question #1 : Sin, Cos, Tan

Calculate $cos(\frac{5\pi}{3})$ .

Possible Answers:

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

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

$-\frac{1}{2}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

First, convert the given angle measure from radians to degrees:

$cos(\frac{5\pi}{3})=cos(300^{\circ})$

Next, recall that $300^{\circ}$ lies in the fourth quadrant of the unit circle, wherein the cosine is positive. Furthermore, the reference angle of $300^{\circ}$ is

$360^{\circ}-300^{\circ}=60^{\circ}$

Hence, all that is required is to recognize from these observations that

$cos(\frac{5\pi}{3})=cos(300^{\circ}) =cos(60^{\circ})$ ,

which is $\frac{1}{2}$ .

Therefore,

$cos(\frac{5\pi}{3})=\frac{1}{2}$

Report an Error

Example Question #1 : Sin, Cos, Tan

What is the result when the following expression is simplified as much as possible?

$\sin(2h)\sec(h)+2\sin(-h)$

Possible Answers:

$2\sin h$

$\sec h$

Correct answer:

Explanation:

Because $\sin x$ is an odd function, we can rewrite the second term in the expression.

$2\sin(-h)=-2\sin h$ .

We now use a double-angle formula to expand the first term.

$\sin(2h)\sec h=2\sin h\cos h\sec h$ .

Because they are reciprocals, $\cos h\sec h=1$ .

$2\sin h\cos h\sec h-2\sin h=2\sin h-2\sin h=0.$

Report an Error

Example Question #2 : Sin, Cos, Tan

Round to the nearest hundredth.

Use your calculator to find:

$\sin72^{\circ}$

Possible Answers:

0.95

0.72

None of the above

0.25

Correct answer:

0.95

Explanation:

Before plugging the function into the calculator make sure the mode of the calculator is set to degrees,

Plug in $\sin72^{\circ}$ which equals to 0.95 .

Report an Error

Example Question #1 : Sin, Cos, Tan

Round to the nearest hundredth.

Use your calculator to find:

$\cos \frac{3\pi}{8}$

Possible Answers:

0.38

0.95

None of the above

Correct answer:

0.38

Explanation:

Before plugging the function into the calculator make sure the mode of the calculator is set to radians,

plug in

$\cos \frac{3\pi}{8}$

which is equal to 0.38 .

Report an Error

View Trigonometry Tutors

Dejuan
Certified Tutor

University of Illinois at Urbana-Champaign, Bachelor of Science, Electrical Engineering.

View Trigonometry Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

View Trigonometry Tutors

Yucheng
Certified Tutor

The University of Texas at Austin, 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

GRE Courses & Classes in Los Angeles, GRE Courses & Classes in Miami, Spanish Courses & Classes in Miami, LSAT Courses & Classes in Chicago, MCAT Courses & Classes in Phoenix, SAT Courses & Classes in Philadelphia, SAT Courses & Classes in Atlanta, SSAT Courses & Classes in Denver, ISEE Courses & Classes in Philadelphia, SSAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

ISEE Test Prep in New York City, ACT Test Prep in Dallas Fort Worth, GMAT Test Prep in Boston, SSAT Test Prep in Atlanta, GRE Test Prep in Washington DC, GMAT Test Prep in New York City, ISEE Test Prep in Chicago, ISEE Test Prep in Philadelphia, MCAT Test Prep in San Diego, MCAT Test Prep in Dallas Fort Worth

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 : Sin, Cos, Tan

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #1 : Trigonometry

Example Question #1 : Sin, Cos, Tan

Example Question #1 : Sin, Cos, Tan

Example Question #2 : Sin, Cos, Tan

Example Question #2 : Sine, Cosine, & Tangent

Example Question #4 : Sin, Cos, Tan

Example Question #1 : Sin, Cos, Tan

Example Question #1 : Sin, Cos, Tan

Example Question #2 : 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: