Call Now to Set Up Tutoring:

(888) 888-0446

Trigonometry : Simplifying Trigonometric Functions

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 #94 : Trigonometry

Simplify the following trionometric function:

$\frac{4sin^2(60^{\circ})-tan(45^{\circ})}{3sin(45^{\circ})}$

Possible Answers:

1/2

$\sqrt{2}/2$

3/4

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

Correct answer:

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

Explanation:

To solve the problem, you need to know the following information:

$sin(60^{\circ}) = \frac{\sqrt{3}}{2}$

$tan(45^{\circ})=1$

$sin(45^{\circ})=\frac{\sqrt{2}}{2}$

Replace the trigonometric functions with these values:

$\frac{4sin^2(60^{\circ})-tan(45^{\circ})}{3sin(45^{\circ})}$

$\frac{4(\frac{\sqrt{3}}{2})^2-(1)}{3(\frac{\sqrt{2}}{2})}$

$\frac{4(\frac{3}{4})-(1)}{(\frac{3\sqrt{2}}{2})}$

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

$\frac{4}{3\sqrt{2}} = \frac{4\cdot \sqrt{2}}{3\sqrt{2}\cdot \sqrt{2}} = \frac{4\sqrt{2}}{6} = \frac{2\sqrt{2}}{3}$

Report an Error

Example Question #1 : Simplifying Trigonometric Functions

Simplify the following trigonometric function in fraction form:

$cos^{2}(45^{\circ})-sin(30^{\circ})$

Possible Answers:

1/3

1/2

Correct answer:

Explanation:

To determine the value of the expression, you must know the following trigonometric values:

$cos(45^{\circ}) = \frac{\sqrt{2}}{2}$

$sin (30^{\circ})=\frac{1}{2}$

Replacing these values, we get:

$cos^{2}(45^{\circ})-sin(30^{\circ})$

$(\frac{\sqrt{2}}{2})^{2}-\frac{1}{2}$

$\frac{2}{4}-\frac{1}{2}=\frac{1}{2}-\frac{1}{2}=0$

Report an Error

Example Question #3 : Simplifying Trigonometric Functions

$tan (x)*sin(x) + sec(x)*(cos x)^{2} =$

Possible Answers:

sec (x)

csc (x)

cos (x)* sin (x)

$(cos x)^{2}$

tan (x)

Correct answer:

sec (x)

Explanation:

$tan (x)*sin(x) + sec(x)*(cos x)^{2} =$

$\frac{sin (x)}{cos (x)}* sin(x) + \frac{1}{cos (x)}*(cos x)^{2} =$

$\frac{(sin x)^{2} + (cos x)^{2}}{cos (x)} = \frac{1}{cos (x)} = sec (x)$

Report an Error

Example Question #4 : Simplifying Trigonometric Functions

Simplify the following expression:

$A=cos(\frac{3\pi}{2}+x)+sin (\pi+x)+cos(\frac{\pi}{2}+x)+sin(\pi-x)$

Possible Answers:

A=-1

$A=-sin\ x$

A=1

A=0

$A=sin\ x$

Correct answer:

A=0

Explanation:

We need to use the following identities:

$cos(\frac{3\pi}{2}+x)=sin\ x$

$sin (\pi+x)=-sin\ x$

$cos(\frac{\pi}{2}+x)=-sin\ x$

$sin(\pi-x)=sin\ x$

Use these to simplify the expression as follows:

$A=cos(\frac{3\pi}{2}+x)+sin (\pi+x)+cos(\frac{\pi}{2}+x)+sin(\pi-x)$

$\Rightarrow A=sin\ x-sin\ x-sin\ x+sin\ x = 0$

Report an Error

Example Question #5 : Simplifying Trigonometric Functions

Give the value of :

$A=\frac{2sin(\frac{\pi}{2})+4cos(\frac{\pi}{2})}{4sin(\frac{\pi}{2})-cos(\frac{\pi}{2})}$

Possible Answers:

A=0

A=1.5

A=1

A=2

A=0.5

Correct answer:

A=0.5

Explanation:

$sin(\frac{\pi}{2})=1$

$cos(\frac{\pi}{2})=0$

Plug these values in:

$A=\frac{2sin(\frac{\pi}{2})+4cos(\frac{\pi}{2})}{4sin(\frac{\pi}{2})-cos(\frac{\pi}{2})}=\frac{2\times 1+4\times 0}{4\times 1-0}=\frac{2}{4}=\frac{1}{2}=0.5$

Report an Error

Example Question #3 : Simplifying Trigonometric Functions

If $tan\ x = \frac{1}{4}$ , solve for

$D=\frac{sin\ x}{sin\ x-cos\ x}+\frac{sin\ x+cos\ x}{cos\ x}$

Possible Answers:

$D=\frac{11}{12}$

$D=\frac{7}{12}$

$D=-\frac{11}{12}$

$D=\frac{1}{12}$

$D=\frac{5}{12}$

Correct answer:

$D=\frac{11}{12}$

Explanation:

$tan\ x=\frac{1}{4}\Rightarrow \frac{sin\ x}{cos\ x}=\frac{1}{4}\Rightarrow cos\ x=4sin\ x$

Substitute $cos\ x=4sin \ x$ into the expression:

$D=\frac{sin\ x}{sin\ x-cos\ x}+\frac{sin\ x+cos\ x}{cos\ x}=\frac{sin\ x}{sin\ x-4sin\ x}+\frac{sin\ x+4sin\ x}{4sin\ x}$

$\Rightarrow D=\frac{sin\ x}{-3sin\ x}+\frac{5sin\ x}{4sin\ x}$

$\Rightarrow D=-\frac{1}{3}+\frac{5}{4}=\frac{-4+15}{12}=\frac{11}{12}$

Report an Error

Example Question #2 : Simplifying Trigonometric Functions

If $cot\ x= 3$ , give the value of :

$D=\frac{cos^2x}{(sin\ x)(cos\ x)}-\frac{sin\ x+cos\ x}{sin\ x}$

Possible Answers:

D=-2

D=-1

D=0

D=1

D=2

Correct answer:

D=-1

Explanation:

$cot\ x=3\Rightarrow \frac{cos\ x}{sin\ x}=3\Rightarrow cos\ x= 3sin\ x$

Now substitute $cos\ x=3sin\ x$ into the expression:

$D=\frac{cos^2x}{(sin\ x)(cos\ x)}-\frac{sin\ x+cos\ x}{sin\ x}=\frac{(3sin\ x)^2}{(sin\ x)(3sin\ x)}-\frac{sin\ x+3sin\ x}{sin\ x}$

$\Rightarrow D=\frac{9sin^2x}{3sin^2x}-\frac{4sin\ x}{sin\ x}$

$\Rightarrow D=\frac{9}{3}-4=3-4=-1$

Report an Error

Example Question #3 : Simplifying Trigonometric Functions

Simplify the following expression:

$A=\frac{sin^2x}{1+tan^2x}-\frac{cos^2x}{1+cot^2x}+1$

Possible Answers:

A=-2

A=1

A=2

A=-1

A=0

Correct answer:

A=1

Explanation:

We need to use the following identitities:

$\frac{1}{cos ^2x}=1+tan^2x$

$\frac{1}{sin^2x}=1+cot^2x$

Now substitute them into the expression:

$A=\frac{sin^2x}{1+tan^2x}-\frac{cos^2x}{1+cot^2x}+1=\frac{sin^2x}{\frac{1}{cos^2x}}-\frac{cos^2x}{\frac{1}{sin^2x}}+1$

$\Rightarrow A=(sin^2x)(cos^2x)-(sin^2x)(cos^2x)+1=0+1=1$

Report an Error

Example Question #1 : Simplifying Trigonometric Functions

If $cos\ x=\frac{1}{3}$ and $sin\ x\neq 0$ , give the value of $\frac{sin\ x+sin\ 2x}{sin\ x-sin\ 2x}$ .

Possible Answers:

Correct answer:

Explanation:

Based on the double angle formula we have, $sin\ 2x=2(sin\ x)(cos\ x)$ .

$\frac{sin\ x+sin\ 2x}{sin\ x-sin\ 2x}=\frac{sin\ x+2(sin\ x)(cos\ x)}{sin\ x-2(sin\ x)(cos\ x)}$

$=\frac{sinx(1+2cos\ x )}{sinx(1-2cos\ x )}=\frac{1+2cos\ x}{1-2cos\ x}$

$=\frac{1+2(\frac{1}{3})}{1-2(\frac{1}{3})}=\frac{\frac{3+2}{3}}{\frac{3-2}{3}}=5$

Report an Error

Example Question #1 : Simplifying Trigonometric Functions

If $x=\frac{\pi}{3}$ , give the value of $\frac{sin\ x}{sin\ x+cos\ 2x}$ .

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

$x=\frac{\pi}{3}\Rightarrow sin\ x=sin(\frac{\pi}{3})=\frac{\sqrt{3}}{2}$

Now we can write:

$x=\frac{\pi}{3}\Rightarrow 2x=2(\frac{\pi}{3})=\frac{2\pi}{3}\Rightarrow cos\ 2x=cos(\frac{2\pi}{3})$

$=cos(\pi-\frac{\pi}{3})$

$=-cos (\frac{\pi}{3})$

$=-\frac{1}{2}$

Now we can substitute the values:

$\frac{sin\ x}{sin\ x+cos\ 2x}=\frac{\frac{\sqrt{3}}{2}}{\frac{\sqrt{3}}{2}-\frac{1}{2}}=\frac{\sqrt{3}}{\sqrt{3}-1}=\frac{\sqrt{3}}{\sqrt{3}-1}\times \frac{{\sqrt{3}+1}}{{\sqrt{3}+1}}=\frac{3+\sqrt{3}}{2}$

Report an Error

View Trigonometry Tutors

James
Certified Tutor

St. Mary of the Plains College, Bachelors, Mathematics. Baker University, Masters, Business Administration and Management.

View Trigonometry Tutors

Ivory
Certified Tutor

Hopkinsville Community College, Associate, Associates in Science. Western Kentucky University, Bachelor in Arts, Psychology.

View Trigonometry Tutors

Ian
Certified Tutor

Lipscomb University, Bachelor of Science, Biology, General.

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

SAT Courses & Classes in San Diego, SSAT Courses & Classes in Phoenix, Spanish Courses & Classes in Philadelphia, LSAT Courses & Classes in Houston, LSAT Courses & Classes in Philadelphia, ACT Courses & Classes in Chicago, ACT Courses & Classes in Seattle, ISEE Courses & Classes in Denver, GRE Courses & Classes in Los Angeles, ACT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

ISEE Test Prep in Boston, MCAT Test Prep in Boston, SAT Test Prep in San Diego, SSAT Test Prep in Denver, ISEE Test Prep in New York City, GRE Test Prep in San Francisco-Bay Area, GMAT Test Prep in New York City, SSAT Test Prep in Phoenix, GMAT Test Prep in Seattle, GRE Test Prep in New York City

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 : Simplifying Trigonometric Functions

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #94 : Trigonometry

Example Question #1 : Simplifying Trigonometric Functions

Example Question #3 : Simplifying Trigonometric Functions

Example Question #4 : Simplifying Trigonometric Functions

Example Question #5 : Simplifying Trigonometric Functions

Example Question #3 : Simplifying Trigonometric Functions

Example Question #2 : Simplifying Trigonometric Functions

Example Question #3 : Simplifying Trigonometric Functions

Example Question #1 : Simplifying Trigonometric Functions

Example Question #1 : Simplifying Trigonometric Functions

All Trigonometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: