Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Sine

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

← Previous 1 2 3 4 5 Next →

Example Question #1 : Sine

What is the period of 2sin(4Θ)?

Possible Answers:

None of the answers are correct

$\frac{\pi}{2}$

$2\pi$

Correct answer:

$\frac{\pi}{2}$

Explanation:

The period of sinΘ is 2Π, so we set the new angle equal to the base period of 2Π and solve for Θ.

So 4Θ = 2Π and Θ = Π/2.

Report an Error

Example Question #2 : Sine

A function with period P will repeat on intervals of length P, and these intervals are referred to as periods.

Find the period of

$sin\, (\pi x)$ .

Possible Answers:

$\pi$

$4\pi$

$2\pi$

Correct answer:

Explanation:

For the function

$sin\, (Ax)$

the period is equal to

$\frac{2\pi}{A}$

in this case

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

which reduces to .

Report an Error

Example Question #1 : How To Find The Period Of The Sine

A function with period P will repeat on intervals of length P, and these intervals are referred to as periods.

Find the period of the function

$\sin \bigg(\frac{1}{2}x\bigg)$ .

Possible Answers:

$\pi$

$4\pi$

$\frac{1}{2}$

Correct answer:

$4\pi$

Explanation:

For the function

$sin\, (Ax)$

the period is equal to

$\frac{2\pi}{A}$

in this case

$\frac{2\pi}{\frac{1}{2}}=2\pi \cdot \frac{2}{1}$

which reduces to $4\pi$ .

Report an Error

Example Question #4 : Sine

What is the period of the function $f(t) = -2\sin(4t)$ ?

Possible Answers:

$-\pi$

$2\pi$

$\frac{\pi}{2}$

Correct answer:

$\frac{\pi}{2}$

Explanation:

To find the period of Sine and Cosine functions you use the formula:
$\frac{2\pi}{\left | b\right |}$ where comes from $f(t) = a\sin(bt)$ . Looking at our formula you see b is 4 so
$\frac{2\pi}{\left | 4\right |}=\frac{\pi}{2}$

Report an Error

Example Question #5 : Sine

What is the period of the given trigonometric function:

$c(t) = 3\sin(-2t)$ . Leave your answer in terms of $\pi$ , simplify all fractions.

Possible Answers:

$\frac{\pi}{3}$

$\frac{\pi}{2}$

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

$\pi$

$-\pi$

Correct answer:

$\pi$

Explanation:

To find the period of a sine, cosine, cosecant, or secant funciton use the formula:

$\omega = \frac{2\pi}{\left|b\right|}$ where comes from the general formula: $c(t)=a\sin(bt)$ . We see that for our equation $\left|b\right| = 2$ and so the period is $\pi$ when you reduce the fraction.

Report an Error

Example Question #51 : Trigonometry

Find the period of the following formula:

$f(x)=2\sin(4\theta)$

Possible Answers:

$\frac{2}{\pi}$

$\pi$

$2\pi$

$\frac{1}{\pi}$

$\frac{\pi}{2}$

Correct answer:

$\frac{\pi}{2}$

Explanation:

To find period, simply remember the following formula:

$\textup{period}=\frac{2\pi}{B}$

where B is the coefficient in front of x. Thus,

$\textup{period}=\frac{2\pi}{4}=\frac{\pi}{2}$

Report an Error

Example Question #7 : Sine

Find the domain of the function: $y=-9\sin(5\theta-3)-3$

Possible Answers:

$\left(-\frac{2\pi}{5},\infty\right)$

$\left(-\frac{2\pi}{5},\frac{2\pi}{5}\right)$

$\left[-\frac{2\pi}{5},\frac{2\pi}{5}\right]$

$\left(-\frac{5}{3},\frac{2\pi}{5}\right)$

${}(-\infty,\infty)$

Correct answer:

${}(-\infty,\infty)$

Explanation:

The function $y=-9\sin(5\theta-3)-3$ is related to the parent function $y=\sin(\theta)$ , which has a domain of $(-\infty.\infty)$ .

The value of theta for $y=-9\sin(5\theta-3)-3$ has no restriction and is valid for all real numbers.

The answer is $(-\infty,\infty)$ .

Report an Error

Example Question #8 : Sine

What is the domain of the given trigonometric function:

$z(t) = 2\sin(-2t)$

Possible Answers:

[-2,2]

$[-\pi,\pi]$

$(-\infty,\infty)$

[-2,0]

$[0,\infty]$

Correct answer:

$(-\infty,\infty)$

Explanation:

For both Sine and Cosine, since there are no asymptotes like Tangent and Cotangent functions, the function can take in any value for . Thus the domain is:

$(-\infty,\infty)$

Report an Error

Example Question #9 : Sine

Which of the following statements is (are) true:

I. The domain of the tangent function is all real numbers

II. The range of the sine function is all real numbers

III. The periods of the tangent, sine, and cosine functions are the same.

Possible Answers:

II only

I only

I and II only

none of the above

II and III only

Correct answer:

II only

Explanation:

The domain of the tangent function does not include any values of x that are odd multiples of π/2 .

The range of the sine function is from [-1, 1].

The period of the tangent function is π, whereas the period for both sine and cosine is 2π.

Report an Error

Example Question #10 : Sine

Which of the following represents a sine wave with a range of $-5 \leq y \leq 5$ ?

Possible Answers:

f(x)=sin(5x)

f(x)=5sin(x) + 3

f(x)=5sin(3x)

f(x)=sin(x)+5

f(x)=5sin(x)+5

Correct answer:

f(x)=5sin(3x)

Explanation:

The range of a sine wave is altered by the coefficient placed in front of the base equation. So, if you have f(x)=5sin(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)=5sin(x)+5 , 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, then, it is fine to use f(x)=5sin(3x) . The for the function parameter only alters the period of the equation, making its waves "thinner."

Report an Error

← Previous 1 2 3 4 5 Next →

View ACT Math Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View ACT Math Tutors

Whitney
Certified Tutor

Mississippi State University, Bachelor of Education, Elementary School Teaching. Walden University, Master of Science, Mathem...

View ACT Math Tutors

Sharon
Certified Tutor

Tabor College, Bachelor of Science, Mathematics Teacher Education. Tabor College, Masters in Education, Education.

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

Spanish Courses & Classes in Chicago, LSAT Courses & Classes in Phoenix, SSAT Courses & Classes in Seattle, ACT Courses & Classes in Houston, SAT Courses & Classes in San Diego, Spanish Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Philadelphia, ACT Courses & Classes in Phoenix, MCAT Courses & Classes in Philadelphia, ISEE Courses & Classes in New York City

Popular Test Prep

MCAT Test Prep in Dallas Fort Worth, SAT Test Prep in Boston, ACT Test Prep in Philadelphia, SAT Test Prep in Denver, SSAT Test Prep in Atlanta, ACT Test Prep in New York City, SSAT Test Prep in Miami, SAT Test Prep in Seattle, SAT Test Prep in San Diego, SSAT Test Prep in Boston

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 : Sine

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Sine

Example Question #2 : Sine

Example Question #1 : How To Find The Period Of The Sine

Example Question #4 : Sine

Example Question #5 : Sine

Example Question #51 : Trigonometry

Example Question #7 : Sine

Example Question #8 : Sine

Example Question #9 : Sine

Example Question #10 : Sine

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: