We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Graphs and Inverses of Trigonometric Functions

Study concepts, example questions & explanations for Precalculus

Create An Account

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Law Of Cosines

A triangle has sides of length 12, 17, and 22. Of the measures of the three interior angles, which is the greatest of the three?

Possible Answers:

$97.2^{\circ }$

$130.1^{\circ }$

$93.6^{\circ }$

$86.4^{\circ }$

$119.2^{\circ }$

Correct answer:

$97.2^{\circ }$

Explanation:

We can apply the Law of Cosines to find the measure of this angle, which we will call :

$c^{2} = a^{2} + b^{2} -2ab \cos C$

The widest angle will be opposite the side of length 22, so we will set:

c=22 , a=12 , b=17

$22^{2} = 12^{2} + 17^{2} -2\cdot 12\cdot 17 \cos C$

$484 = 144 + 289 -408 \cos C$

$51= -408 \cos C$

$\cos C = -\frac{51}{408} = -0.125$

$C = \cos^{-1} 0.125 = 97.2^{\circ }$

Report an Error

Example Question #11 : Graphing The Sine And Cosine Functions

In $\Delta ABC$ , $m \angle A = 66^{\circ }$ , AB = 26 , and AC = 23 . To the nearest tenth, what is ?

Possible Answers:

41.1

A triangle with these characteristics cannot exist.

26.8

47.9

112.4

Correct answer:

26.8

Explanation:

By the Law of Cosines:

$\left ( BC\right )^{2} = \left ( AB\right )^{2} + \left ( AC\right )^{2} - 2 \cdot AB \cdot AC \cdot \cos m \angle A$

or, equivalently,

$BC =\sqrt{ \left ( AB\right )^{2} + \left ( AC\right )^{2} - 2 \cdot AB \cdot AC \cdot \cos m \angle A}$

Substitute:

$BC =\sqrt{ 26^{2} +23^{2} - 2 \cdot 26 \cdot 23 \cdot \cos 66 ^{\circ }}$

$\approx \sqrt{ 676 +529 - 1,196 \cdot 0.4067}$

$\approx \sqrt{ 718.6} \approx 26.8$

Report an Error

Example Question #1 : Trigonometric Functions And Graphs

What is the period of

$\tan \left ( \frac{x}{\pi } \right )$ ?

Possible Answers:

$2\pi$

$\frac{1}{\pi }$

$\pi$

$\pi^{2}$

Correct answer:

$\pi^{2}$

Explanation:

The period for $\tan(x)$ is $\pi$ . However, if a number is multiplied by , you divide the period $\pi$ by what is being multiplied by . Here, $(1/\pi )$ is being multiplied by . $\pi/(1/\pi )$ equals $\pi^{2}$ .

Report an Error

Example Question #12 : Graphing The Sine And Cosine Functions

Which of the following is not in the range of the function $y = \sin{x}$ ?

Possible Answers:

$\frac{3}{4}$

$\frac{3}{2}$

$\frac{2}{3}$

$-\frac{1}{2}$

Correct answer:

$\frac{3}{2}$

Explanation:

The range of the function $y= \sin x$ is all numbers between and (the sine wave never goes above or below this).

Of the choices given, $\frac{3}{2}$ is greater than and thus not in this range.

Report an Error

Example Question #1 : Using Basic And Definitional Identities

Trig_id

What is the $\sin$ of $\theta$ ?

Possible Answers:

$\frac{h}{o}$

$\frac{o}{h}$

$\frac{h}{a}$

$\frac{o}{a}$

$\frac{a}{h}$

Correct answer:

$\frac{o}{h}$

Explanation:

When working with basic trigonometric identities, it's easiest to remember the mnemonic: SOHCAHTOA .

$\sin=\frac{opposite}{hypotenuse}$

$\cos=\frac{adjacent}{hypotenuse}$ ,

$\tan=\frac{opposite}{adjacent}$

When one names the right triangle, the opposite side is opposite to the angle, the adjacent side is next to the angle, and the hypotenuse spans the two legs of the right angle.

Report an Error

Example Question #2 : Using Basic And Definitional Identities

Trig_id

What is the $\cos$ of $\theta$ ?

Possible Answers:

$\frac{a}{h}$

$\frac{o}{a}$

$\frac{o}{h}$

$\frac{h}{o}$

$\frac{h}{a}$

Correct answer:

$\frac{a}{h}$

Explanation:

When working with basic trigonometric identities, it's easiest to remember the mnemonic: SOHCAHTOA .

$\sin=\frac{opposite}{hypotenuse}$

$\cos=\frac{adjacent}{hypotenuse}$ ,

$\tan=\frac{opposite}{adjacent}$

When one names the right triangle, the opposite side is opposite to the angle, the adjacent side is next to the angle, and the hypotenuse spans the two legs of the right angle.

Report an Error

Example Question #1 : Solving Trigonometric Equations

In a right triangle, if

$cos(x)=\frac{3}{5}$

and

$cos(y)=\frac{4}{5}$

then what does $\tan(x)$ equal?

Possible Answers:

$\frac{4}{3}$

$\frac{3}{4}$

$\frac{3}{5}$

$\frac{5}{4}$

Correct answer:

$\frac{4}{3}$

Explanation:

One can draw a right triangle with acute angles $\angle x$ and $\angle y$ . The side adjacent to $\angle y$ is 4, and the side adjacent to $\angle x$ is 3.

$tan(x)=\frac{opposite}{adjacent}$

Report an Error

Example Question #12 : Graphing The Sine And Cosine Functions

Bob manages a pizza store. He bought a new machine that tracks how big his employees are cutting the pizza slices. The machine measures the average angle size of each slice of each pizza. Unfortunately, the angle is given as 0.7854 radians which Bob does not understand. Help Bob by converting the radian angle into degrees. In degrees, what is the size of the angle for an average pizza slice.

Possible Answers:

$25^{\circ}$

$30^{\circ}$

$75^{\circ}$

$60^{\circ}$

$45^{\circ}$

Correct answer:

$45^{\circ}$

Explanation:

To convert we use a common conversion amount. It may be easiest to remember the full circle example. In degrees, a full circle is $360^{\circ}$ around. In terms of radians, a full circle is $2\pi$ . So to get our answer

$0.7854\ \text{Radians} *\frac{360^{\circ}}{2\pi\ \text{Radians}}= 45^{\circ}$

Report an Error

Example Question #13 : Graphing The Sine And Cosine Functions

Convert $120^{\circ}$ into radians.

Possible Answers:

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

$2\pi$

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

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

$\pi$

Correct answer:

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

Explanation:

To convert from degrees to radians, one multiplies by $\frac{\pi }{180}$ .

$120\cdot \frac{\pi }{180}=\frac{2\pi}{3}$

Report an Error

Example Question #1 : Understanding Angles In The Unit Circle

In the unit circle, what is the angle in radians that corresponds to the point (0, -1)?

Possible Answers:

$2\pi$

$\frac{\pi }{2}$

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

$\pi$

Correct answer:

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

Explanation:

On the unit circle, (0,-1) is the point that falls between the third and fourth quadrant. This corresponds to $\frac{3\pi }{2}$ .

Report an Error

View Pre-Calculus Tutors

Dejuan
Certified Tutor

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

View Pre-Calculus Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

View Pre-Calculus Tutors

Yucheng
Certified Tutor

The University of Texas at Austin, Bachelor of Science, Mechanical Engineering.

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

MCAT Tutors in Miami, GMAT Tutors in Phoenix, ACT Tutors in Dallas Fort Worth, Calculus Tutors in San Diego, Algebra Tutors in Dallas Fort Worth, Spanish Tutors in Atlanta, Spanish Tutors in Seattle, ISEE Tutors in Miami, ISEE Tutors in Chicago, LSAT Tutors in Phoenix

Popular Courses & Classes

ACT Courses & Classes in San Diego, LSAT Courses & Classes in Atlanta, LSAT Courses & Classes in Los Angeles, LSAT Courses & Classes in San Diego, MCAT Courses & Classes in Houston, SAT Courses & Classes in San Diego, Spanish Courses & Classes in Phoenix, GRE Courses & Classes in Atlanta, SSAT Courses & Classes in Denver, SSAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

LSAT Test Prep in Washington DC, GRE Test Prep in Atlanta, SSAT Test Prep in Boston, ISEE Test Prep in San Francisco-Bay Area, SSAT Test Prep in Washington DC, GMAT Test Prep in Phoenix, SSAT Test Prep in Seattle, SSAT Test Prep in San Diego, ACT Test Prep in San Diego, ACT Test Prep in Phoenix

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

Precalculus : Graphs and Inverses of Trigonometric Functions

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Law Of Cosines

Example Question #11 : Graphing The Sine And Cosine Functions

Example Question #1 : Trigonometric Functions And Graphs

Example Question #12 : Graphing The Sine And Cosine Functions

Example Question #1 : Using Basic And Definitional Identities

Example Question #2 : Using Basic And Definitional Identities

Example Question #1 : Solving Trigonometric Equations

Example Question #12 : Graphing The Sine And Cosine Functions

Example Question #13 : Graphing The Sine And Cosine Functions

Example Question #1 : Understanding Angles In The Unit Circle

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: