We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Trigonometry

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 #4 : How To Find The Period Of The Cosine

A function with period will repeat its solutions in intervals of length .

What is the period of the function f(x) = cos(x) +3 ?

Possible Answers:

$3\pi$

$2\pi$

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

Correct answer:

$2\pi$

Explanation:

For a trigonometric function $f(x) = \alpha cos(bx -c) +d$ , the period is equal to $\frac{2\pi}{b}$ . So, for f(x) = cos(x) +3 , $P = \frac{2\pi}{1} = 2\pi$ .

Report an Error

Example Question #41 : Cosine

A function with period will repeat its solutions in intervals of length .

What is the period of the function $f(x) = 3cos(4\pi x-4) -2$ ?

Possible Answers:

$8\pi^2$

$\frac{1}{2}$

$4\pi$

$\frac{\pi}{2}$

$2\pi$

Correct answer:

$\frac{1}{2}$

Explanation:

For a trigonometric function $f(x) = \alpha cos(bx -c) +d$ , the period is equal to $\frac{2\pi}{b}$ . So, for $f(x) = 3cos(4\pi x-4) -2$ , $P = \frac{2\pi}{4\pi} = \frac{1}{2}$ .

Report an Error

Example Question #141 : Trigonometry

A function with period will repeat its solutions in intervals of length .

What is the period of the function $f(x) = 2cos(\frac{1}{2}\pi x)$ ?

Possible Answers:

$\pi$

$4\pi$

$2\pi$

Correct answer:

Explanation:

For a trigonometric function $f(x) = \alpha cos(bx -c) +d$ , the period is equal to $\frac{2\pi}{b}$ . So, for $f(x) = 2cos(\frac{1}{2}\pi x)$ , $P = \frac{2\pi}{\frac{1}{2}\pi} = 4$ .

Report an Error

Example Question #1 : How To Find The Range Of The Cosine

Simplify (cosΘ – sinΘ)²

Possible Answers:

1 + cos2Θ

1 – sin2Θ

cos2Θ – 1

sin2Θ – 1

1 + sin2Θ

Correct answer:

1 – sin2Θ

Explanation:

Multiply out the quadratic equation to get cosΘ² – 2cosΘsinΘ + sinΘ²

Then use the following trig identities to simplify the expression:

sin2Θ = 2sinΘcosΘ

sinΘ² + cosΘ² = 1

1 – sin2Θ is the correct answer for (cosΘ – sinΘ)²

1 + sin2Θ is the correct answer for (cosΘ + sinΘ)²

Report an Error

Example Question #1 : How To Find The Range Of The Cosine

Which of the following represents a cosine function with a range of to ?

Possible Answers:

f(x)=cos(x)-30

f(x)=18cos(2x)-30

f(x)=cos(18x)-30

f(x)=4cos(9x)-12

f(x)=9cos(22x)-21

Correct answer:

f(x)=9cos(22x)-21

Explanation:

The range of a cosine wave is altered by the coefficient placed in front of the base equation. So, if you have f(x)=12cos(x) , this means that the highest point on the wave will be at and the lowest at ; however, if you then begin to shift the equation vertically by adding values, as in, f(x)=12cos(x)+1 , then you need to account for said shift. This would make the minimum value to be and the maximum value to be .

For our question, the range of values covers |-30-(-12)|=|-30+12|=18 . This range is accomplished by having either or as your coefficient. ( merely flips the equation over the -axis. The range "spread" remains the same.) We need to make the upper value to be instead of . To do this, you will need to subtract 9+12 , or , from . This requires an downward shift of . An example of performing a shift like this is:

f(x)=cos(x)-21

Among the possible answers, the one that works is:

f(x)=9cos(22x)-21

The 22x parameter does not matter, as it only alters the frequency of the function.

Report an Error

Example Question #1 : How To Find The Range Of The Cosine

Which of the following represents a cosine function with a range from to ?

Possible Answers:

f(x)=-13cos(x)+8

f(x)=12cos(x)+21

f(x)=cos(13x)+8

f(x)=13cos(x)+21

f(x)=-26cos(x)+8

Correct answer:

f(x)=-13cos(x)+8

Explanation:

For our question, the range of values covers |-5-21|=|-26|=26 . This range is accomplished by having either or as your coefficient. ( merely flips the equation over the -axis. The range "spread" remains the same.) We need to make the upper value to be instead of . This requires an upward shift of . An example of performing a shift like this is:

f(x)=cos(x)+8

Among the possible answers, the one that works is:

f(x)=-13cos(x)+8

Report an Error

Example Question #4 : How To Find The Range Of The Cosine

What is the range of the trigonometric function defined by $S(t) = -3\sin (1.5t)$ ?

Possible Answers:

[-1.5,1.5]

[1.5,3]

[-3,3]

[0,3]

[-3,1.5]

Correct answer:

[-3,3]

Explanation:

The range of a sine or cosine function spans from the negative amplitude to the positive amplitutde. The amplutide is given by $\left|a\right|$ in the equation $S(t)=a\sin(bt)$ . Thus the range for our function is [-3,3]

Report an Error

Example Question #1 : How To Find The Range Of The Cosine

What is the range of the given trigonometric equation:

$f(t) = \cos(-3t)$

Possible Answers:

[-3,3]

[0,3]

$(-\infty,\infty)$

$[0,\infty)$

[-1,1]

Correct answer:

[-1,1]

Explanation:

For the sine and cosine funcitons, the range is equal to the negative amplitude to the positive amplitude.

The amplitude is found by taking $\left|a\fight|$ from the general equation:

$f(t) = a\cos(bt)$ .

We see in our equation that $a = 1 \rightarrow \left|a\right| = 1$

(when no coefficient is written, it is a 1).

Thus we get that the amplitude is [-1,1]

Report an Error

Example Question #6 : How To Find The Range Of The Cosine

What is the range of the function f (x) = cos (x) + 5 ?

Possible Answers:

$(-\infty, \infty)$

[-6, 6]

[-1, 1]

[4, 6]

There is no valid range for this equation.

Correct answer:

[4, 6]

Explanation:

The range of the function represents the spread of possible answers you can get for f(x) , given all values of . In this case, the ordinary range for a cosine function is [-1, 1] , since the largest value that cosine can solve to is (for a cosine of $0/2\pi/360^{\circ}$ or a multiple of one of those values), and the smallest value cosine can solve to is (for a cosine of $\pi/180^{\circ}$ or a multiple of one of those values).

However, in this case our final answer is increased by after the cosine is applied to . This results in a final range of to (or, in other words, to , plus ).

So, our final range is [4, 6] .

Report an Error

Example Question #7 : How To Find The Range Of The Cosine

What is the range of the function f (x) = -3cos(x) ?

Possible Answers:

$(-\infty, \infty)$

[-4, -2]

$(-3\pi, \pi)$

There is no range that fits this equation.

[-3, 3]

Correct answer:

[-3, 3]

Explanation:

However, in this case our final answer is multiplied by -3 after the cosine is applied to . This results in a final range of to (or, in other words, to , multiplied by ).

So, our final range is [- 3, 3] .

Report an Error

View ACT Math Tutors

Dejuan
Certified Tutor

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

View ACT Math Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

View ACT Math Tutors

Yucheng
Certified Tutor

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

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

SSAT Courses & Classes in Denver, LSAT Courses & Classes in Philadelphia, MCAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in San Diego, ACT Courses & Classes in Boston, SAT Courses & Classes in Seattle, GMAT Courses & Classes in Miami, ISEE Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in San Diego, MCAT Courses & Classes in Miami

Popular Test Prep

ACT Test Prep in New York City, LSAT Test Prep in New York City, ACT Test Prep in San Francisco-Bay Area, GRE Test Prep in Seattle, ACT Test Prep in San Diego, ACT Test Prep in Boston, MCAT Test Prep in Los Angeles, MCAT Test Prep in Phoenix, ISEE Test Prep in Dallas Fort Worth, GRE Test Prep in Washington DC

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 : Trigonometry

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #4 : How To Find The Period Of The Cosine

Example Question #41 : Cosine

Example Question #141 : Trigonometry

Example Question #1 : How To Find The Range Of The Cosine

Example Question #1 : How To Find The Range Of The Cosine

Example Question #1 : How To Find The Range Of The Cosine

Example Question #4 : How To Find The Range Of The Cosine

Example Question #1 : How To Find The Range Of The Cosine

Example Question #6 : How To Find The Range Of The Cosine

Example Question #7 : How To Find The Range Of The Cosine

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: