Call Now to Set Up Tutoring:

(888) 888-0446

Trigonometry : Arcsin, Arccos, Arctan

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 #3 : Graphing The Sine And Cosine Functions

Trig_id

What is $\theta$ if o=10 and a=8 ?

Possible Answers:

$55.14^{\circ}$

$89.60^{\circ}$

$51.34^{\circ}$

$53.14^{\circ}$

$0.90^{\circ}$

Correct answer:

$51.34^{\circ}$

Explanation:

In order to find $\theta$ we need to utilize the given information in the problem. We are given the opposite and adjacent sides. We can then, by definition, find the $\tan$ of $\theta$ and its measure in degrees by utilizing the $\arctan$ function.

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

$\tan=\frac{10}{8}$

$\tan=1.25$

Now to find the measure of the angle using the $\arctan$ function.

$\theta=\arctan1.25$

$\rightarrow 51.34^{\circ}$

If you calculated the angle's measure to be $0.90^{\circ}}$ then your calculator was set to radians and needs to be set on degrees.

Report an Error

Example Question #1 : Arcsin, Arccos, Arctan

Soh_cah_toa

For the above triangle, what is $\theta$ if o = 20 and a = 14 ?

Possible Answers:

$45.6^{\circ}$

$60.0^{\circ}$

$35.0^{\circ}$

$55.0^{\circ}$

$44.4^{\circ}$

Correct answer:

$55.0^{\circ}$

Explanation:

We need to use a trigonometric function to find $\theta$ . We are given the opposite and adjacent sides, so we can use the $\tan$ and $\arctan$ functions.

$\tan(\theta) = \frac{\textup{opposite}}{\textup{adjacent}}$

$\tan(\theta) = \frac{20}{14}$

$\theta = \arctan\left ( \frac{20}{14} \right )$

$\theta = 55.0^{\circ}$

Report an Error

Example Question #2 : Arcsin, Arccos, Arctan

Soh_cah_toa

For the above triangle, what is $\theta$ if o = 17 and h = 25 ?

Possible Answers:

$55.8^{\circ}$

$11.8^{\circ}$

$34.2^{\circ}$

$47.2^{\circ}$

$42.8^{\circ}$

Correct answer:

$42.8^{\circ}$

Explanation:

We need to use a trigonometric function to find $\theta$ . We are given the opposite and hypotenuse sides, so we can use the $\sin$ and $\arcsin$ functions.

$\sin(\theta) = \frac{\textup{opposite}}{\textup{hypotenuse}}$

$\sin(\theta) = \frac{17}{25}$

$\theta = \arcsin\left ( \frac{17}{25} \right )$

$\theta = 42.8^{\circ}$

Report an Error

Example Question #1 : Arcsin, Arccos, Arctan

Which of the following is the degree equivalent of the inverse trigonometric function

$\arccos x=\frac{1}{2}$ ?

Possible Answers:

$60^\circ$

$1^\circ$

$360^\circ$

$2^\circ$

$30^\circ$

Correct answer:

$60^\circ$

Explanation:

The $\arccos$ is the reversal of the cosine function. That means that if $\cos \theta=y$ , then $\arccos y=\theta$ .

Therefore,

$\theta=\arccos\left(\frac{1}{2}\right)=60^\circ$

Report an Error

Example Question #3 : Arcsin, Arccos, Arctan

Assuming the angle in degrees, determine the value of $sin^{-1}(1)-cos^{-1}(1)-tan^{-1}(1)$ .

Possible Answers:

$\textup{The answer cannot be determined.}$

Correct answer:

Explanation:

To evaluate $sin^{-1}(1)-cos^{-1}(1)-tan^{-1}(1)$ , it is necessary to know the existing domain and range for these inverse functions.

Inverse sine:

D: [-1,1]

$R \textup{ (in radians)}: [-\frac{\pi}{2},\frac{\pi}{2}]$

Inverse cosine:

D: [-1,1]

$R\textup{ (in radians)}: [0,\pi]$

Inverse tangent:

$D: \textup{All real numbers.}$

$R\textup{ (in radians)}: (-\frac{\pi}{2},\frac{\pi}{2})$

Evaluate each term. The final answers must return an angle.

$sin^{-1}(1)=\frac{\pi}{2} \textup{ radians}=90 \textup{ degrees}$

$cos^{-1}(1)=0 \textup{ degrees}$

$tan^{-1}(1)=\frac{\pi}{4} \textup{ radians}= 45 \textup{ degrees}$

$sin^{-1}(1)-cos^{-1}(1)-tan^{-1}(1)=90-0-45=45 \textup{ degrees}$

Report an Error

Example Question #4 : Arcsin, Arccos, Arctan

$cos(arcsin(sec \ x)) = 0{}$ ,

what value(s) does take?

Assume that $0\leq x< 2\pi$

Possible Answers:

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

$\frac{\pi}{2}$

$0, \pi$

No real solution.

Correct answer:

$0, \pi$

Explanation:

If $cos(arcsin(sec \ x)) = 0{}$ , then we can apply the cosine inverse to both sides:

$cos^{-1}(cos(arcsin(sec \ x))) = cos^{-1}(0)$

$arcsin(sec \ x)) = \frac{\pi }{2} \ or -\frac{\pi }{2}$

Since cosine and cosine inverse undo each other; we can then apply sine and secant inverse functions to obtain the solution.

${}sin(arcsin(sec \ x))) = sin\left(\frac{\pi }{2} \right)$ and $sin(arcsin(sec \ x))) = sin\left(-\frac{\pi }{2}\right) {}$

sec(x) = 1 and sec(x) = -1

$x = 0, \pi$ are the two solutions.

Report an Error

Example Question #3 : Arcsin, Arccos, Arctan

Calculate Arcsec(2) .

Possible Answers:

$\frac{\pi}{3}$

$\frac{\pi}{3}$ and $\frac{5\pi}{3}$

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

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

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

Correct answer:

$\frac{\pi}{3}$

Explanation:

The arcsecant function takes a trigonometric ratio on the unit circle as its input and results in an angle measure as its output. The given function can therefore be rewritten as

$Arcsec2=Arccos\frac{1}{2}$

and is the angle measure $\Theta$ which, when applied to the cosine function $cos\Theta$ , results in $\frac{1}{2}$ . Notice that the arcsecant function as expressed in the statement of the problem is capitalized; hence, we are looking for the "principal" angle measure, or the one which lies between 0rad and $\pi rad$ . Since $cos(\frac{\pi}3)=\frac{1}{2}$ , and since $\frac{\pi}{3}$ lies between 0rad and $\pi rad$ ,

$Arcsec2=\frac{\pi}{3}$ .

Report an Error

Example Question #4 : Arcsin, Arccos, Arctan

Calculate arctan1 .

Possible Answers:

$\frac{\pi}{2}$

$\frac{\pi}{4}$

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

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

Correct answer:

$\frac{\pi}{4}$

Explanation:

The domain on the argument for is

$-\frac{\pi}{2}<x<\frac{\pi}{2}$ .

The range of the function tanx is not defined at $-\frac{\pi}{2}$ or $\frac{\pi}{2}$ , and so the domain of its inverse, , does not include those values. Hence, we must find the angle between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$ for which tanx=1 .

Since $\frac{sinx}{cosx}=tanx$ , the equation tanx=1 can be rewritten as

$\frac{sinx}{cosx}=1$ ,

sinx=cosx

for some x between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$ .

Now, sinx=cosx when $x=\frac{\pi}{4}$ , since $sin(\frac{\pi}{4})=cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}$ .

Therefore,

$arctan1=\frac{\pi}{4}$ .

Report an Error

View Trigonometry Tutors

John
Certified Tutor

Dartmouth College, Bachelor in Arts, Mathematics and Computer Science. Purdue University-Main Campus, Master of Science, Comp...

View Trigonometry Tutors

Scott
Certified Tutor

University of Illinois at Urbana-Champaign, Bachelor of Science, Mathematics.

View Trigonometry Tutors

Sukwon
Certified Tutor

Vanderbilt University, Bachelor of Science, Economics.

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

LSAT Courses & Classes in Los Angeles, LSAT Courses & Classes in San Diego, ACT Courses & Classes in Chicago, GMAT Courses & Classes in San Diego, MCAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in New York City, Spanish Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in San Diego, ACT Courses & Classes in Los Angeles, ISEE Courses & Classes in Dallas Fort Worth

Popular Test Prep

MCAT Test Prep in Phoenix, MCAT Test Prep in Houston, SSAT Test Prep in Houston, MCAT Test Prep in Boston, ACT Test Prep in Atlanta, LSAT Test Prep in Denver, MCAT Test Prep in Los Angeles, GRE Test Prep in Seattle, ACT Test Prep in Chicago, ISEE 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 : Arcsin, Arccos, Arctan

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #3 : Graphing The Sine And Cosine Functions

Example Question #1 : Arcsin, Arccos, Arctan

Example Question #2 : Arcsin, Arccos, Arctan

Example Question #1 : Arcsin, Arccos, Arctan

Example Question #3 : Arcsin, Arccos, Arctan

Example Question #4 : Arcsin, Arccos, Arctan

Example Question #3 : Arcsin, Arccos, Arctan

Example Question #4 : Arcsin, Arccos, Arctan

All Trigonometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: