Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : ACT Math

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find The Cosine Of An Angle

If $\tan A=\frac{b}{c}$ , where $b>0\ and\ c>0$ and $\frac{\pi }{2}<A<\pi$ ,

then what is $cos\ A$ ?

Possible Answers:

$\frac{b}{\sqrt{c^{2}+b^{2}}}$

$\frac{\sqrt{c^{2}+b^{2}}}{c}$

$\frac{c}{\sqrt{c^{2}+b^{2}}}$

$-\frac{c}{\sqrt{c^{2}+b^{2}}}$

$-\frac{\sqrt{c^{2}+b^{2}}}{c}$

Correct answer:

$-\frac{c}{\sqrt{c^{2}+b^{2}}}$

Explanation:

In the triangle below, the tangent of $\angle A\ is\ \frac{b}{c}$ , or the opposite side of the angle divided by the adjacent side of the angle. According to the Pythagorean

Theorem, the $hypotenuse^{2}=c^{2}+b^{2}$

Thus the hypotenuse equals $\sqrt{b^{2}+c^{2}}$ .

The cosine of an angle is the adjacent side of the angle divided by the hypotenuse of the triangle, giving us $\frac{c}{\sqrt{c^{2}+b^{2}}}$ .

However, since $tanA$ is $\frac{sinA}{cosA}$ , and when $A$ is between $\frac{\pi }{2}\ and\ \pi$ , $sinA$ is positive while $cosA$ is negative. Thus, $c$ is negative, giving us the final answer of $-\frac{c}{\sqrt{c^{2}+b^{2}}}$ . Triangle

Report an Error

Example Question #2 : How To Find The Cosine Of An Angle

What is cos θ?

Screen_shot_2013-07-15_at_9.54.23_pm

Possible Answers:

$\frac{29}{5}$

$\frac{\sqrt{29}}{29}$

$\frac{5}{29}$

$\frac{5\sqrt{29}}{29}$

Correct answer:

$\frac{5\sqrt{29}}{29}$

Explanation:

cos = adjacent/hypotenuse = $\frac{5}{\sqrt{29}}$

To get the radical out of the denominator, we multiply:

$\frac{\sqrt{29}}{\sqrt{29}}\ast\frac{5}{\sqrt{29}}$

$=\frac{5\sqrt{29}}{29}$

Report an Error

Example Question #3 : How To Find The Cosine Of An Angle

What is the cosine of the angle formed between the -axis and the line passing through (4,5) with a slope of 2.5 ? Round to the nearest hundredth.

Possible Answers:

0.14

0.34

0.91

0.4

0.6

Correct answer:

0.14

Explanation:

You do not even need to compute the line for this question. All that you need to do is note that you can make a little right triangle with a height of 2.5 and a base of , which you get from the slope of the line. So, to compute the cosine, you will need to find the hypotenuse using the Pythagorean theorem:

$h=\sqrt{2.5^2+1^2}=\sqrt{7.25}$

So, our little triangle looks like:

Cos1

The cosine will be the adjacent side, , divided by the hypotenuse, $\sqrt{7.25}$ :

$\frac{1}{\sqrt{7.25}}$ , or approximately 0.14 .

Report an Error

Example Question #125 : Trigonometry

What is the $\cos$ of an angle with $\sin \left ( \frac{4}{5} \right )$ ?

Possible Answers:

$\frac{5}{4}$

$\frac{3}{4}$

$\frac{4}{3}$

$\frac{3}{5}$

$\frac{5}{3}$

Correct answer:

$\frac{3}{5}$

Explanation:

Since the sine of the angle is $\frac{4}{5}$ , that means the opposite side of the triangle is and the hypotenuse is . Automatically, you know this is a special 3-4-5 right triangle, and that the missing side is 3. If not, you could also find the 3rd side by doing Pythagorean Theorem. This gives you your answer of $\cos=\frac{3}{5}$

Report an Error

Example Question #3041 : Act Math

Right triangle $\Delta ABC$ has sides AB=5 , BC = 7 and $AC = \sqrt{74}$ . What is the cosine of $\angle A$ ?

Possible Answers:

$\frac{5}{7}$

$\frac{\sqrt{74}}{5}$

$\frac{5}{\sqrt74}$

$\frac{7}{5}$

$\frac{7}{\sqrt{74}}$

Correct answer:

$\frac{5}{\sqrt74}$

Explanation:

SOHCAHTOA tells us that $\textup{cos} = \frac{\textup{adjacent}}{\textup{hypotenuse}}$ , and we know the hypotenuse is the longest side of the triangle, $\sqrt(74)$ . Our adjacent side will be the other side that has as a vertex, AB = 5 .

Thus, $\textup{cos} (A) = \frac{AB}{AC} = \frac{5}{\sqrt{74}}$ .

Report an Error

Example Question #3041 : Act Math

Right triangle $\Delta ABC$ has sides AB=7 , $BC = 5\sqrt{11}$ and AC = 18 . What is the cosine of $\angle A$ ?

Possible Answers:

$\frac{5\sqrt{11}}{18}$

$\frac{7}{5\sqrt{11}}$

$\frac{18}{7}$

$\frac{7}{18}$

$\frac{5\sqrt{11}}{7}$

Correct answer:

$\frac{7}{18}$

Explanation:

SOHCAHTOA tells us that $\textup{cos} = \frac{\textup{adjacent}}{\textup{hypotenuse}}$ , and we know the hypotenuse is the longest side of the triangle, . Our adjacent side will be the other side that has as a vertex, AB = 7 .

Thus, $\textup{cos} (A) = \frac{AB}{AC} = \frac{7}{18}$ .

Report an Error

Example Question #1 : How To Find Positive Cosine

The value of a cosine is positive in which quadrants?

Possible Answers:

The 1st and 3rd

The 3rd only

The 1st and 4th

The 4th only

Correct answer:

The 1st and 4th

Explanation:

The cosine is positive in the 1^st and 4^th quadrants and negative in 2^nd and 3^rd

Report an Error

Example Question #3041 : Act Math

Which of the following is equal to $cos\ x * csc\ x$ ?

Possible Answers:

$cot\ x$

$tan\ x$

$sin \ x* sec\ x$

$sec\ x$

$cot\ x* sec\ x$

Correct answer:

$cot\ x$

Explanation:

Here, we use the SOHCAHTOA ratios and the fact that csc x = 1 / sin x.

Cosine x = adjacent side length / hypotenuse length

Cosecant x = 1 / sin x = hypotenuse / opposite

(Adjacent / hypotenuse) * (hypotenuse / opposite) = Adjacent / opposite = Cotangent x.

Report an Error

Example Question #3 : How To Find Positive Cosine

cos(x)=0.5 and is between and $\pi$ . What is the value of cos(0.5x) ?

Possible Answers:

0.25

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

$\sqrt{2}$

$3\sqrt{3}$

Correct answer:

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

Explanation:

For to $\pi$ , we know that $cos(\frac{\pi}{3}) = 0.5$ . So, the question asks, what is the value of cos(0.5x) , where $x=\frac{\pi}{3}$ . Therefore, it is asking what the value of $cos(\frac{\pi}{6})$ is, which is $\frac{\sqrt{3}}{2}$ .

Report an Error

Example Question #2 : How To Find Positive Cosine

To the nearest , what is the cosine formed from the origin to (5, 6) ? Assume counterclockwise rotation.

Possible Answers:

Correct answer:

Explanation:

If the point to be reached is (5, 6) , then we may envision a right triangle with sides and , and hypotenuse . The Pythagorean Theorem tells us that a^2 + b^2 = c^2 , so we plug in and find that: 5^2 + 6^2 = c^2 = 61

Thus, $c = \sqrt{61}$

Now, SOHCAHTOA tells us that $\textup{cosine} = \frac{\textup{adjacent}}{\textup{hypotenuse}}$ , so we know that:

$\textup{cos }x^{\circ} = \frac{5}{\sqrt{61}} \approx 0.6402$

Thus, our cosine is approximately .

Report an Error

View ACT Math Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

View ACT Math Tutors

Quang
Certified Tutor

Georgetown University, Bachelor of Science, Finance.

View ACT Math Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

ISEE Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Miami, SSAT Courses & Classes in Seattle, SAT Courses & Classes in Chicago, GMAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Houston, Spanish Courses & Classes in Seattle, GRE Courses & Classes in New York City, MCAT Courses & Classes in Miami, ACT Courses & Classes in Miami

Popular Test Prep

GMAT Test Prep in Los Angeles, SAT Test Prep in Chicago, MCAT Test Prep in Los Angeles, ISEE Test Prep in Washington DC, SAT Test Prep in Atlanta, GRE Test Prep in New York City, GMAT Test Prep in Houston, MCAT Test Prep in Philadelphia, MCAT Test Prep in Chicago, GRE 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

ACT Math : ACT Math

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Find The Cosine Of An Angle

Example Question #2 : How To Find The Cosine Of An Angle

Example Question #3 : How To Find The Cosine Of An Angle

Example Question #125 : Trigonometry

Example Question #3041 : Act Math

Example Question #3041 : Act Math

Example Question #1 : How To Find Positive Cosine

Example Question #3041 : Act Math

Example Question #3 : How To Find Positive Cosine

Example Question #2 : How To Find Positive Cosine

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: