Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Solving Trigonometric Equations

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Trigonometric Equations

If $tanx=\frac{1}{3}$ $\displaystyle tanx=\frac{1}{3}$, find $f(x)=\frac{sin(3\pi +x)+sin(x-\frac{\pi }{2})}{cos(x-\pi )+cos(\frac{3\pi }{2}+x)}$ $\displaystyle f(x)=\frac{sin(3\pi +x)+sin(x-\frac{\pi }{2})}{cos(x-\pi )+cos(\frac{3\pi }{2}+x)}$.

Possible Answers:

-2

-1

Correct answer:

Explanation:

First we need to simplify each term:

$sin(3\pi +x)= -sinx$ $\displaystyle sin(3\pi +x)= -sinx$

$sin(x-\frac{\pi }{2})=cosx$ $\displaystyle sin(x-\frac{\pi }{2})=cosx$

$cos(x-\pi )=- cosx$ $\displaystyle cos(x-\pi )=- cosx$

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

So we will have:

$f(x)=\frac{-sinx-cosx}{-cosx+sinx}$ $\displaystyle f(x)=\frac{-sinx-cosx}{-cosx+sinx}$

Since we have the value of tanx $\displaystyle tanx$, we can divide the numerator and denominator by cosx $\displaystyle cosx$.

$f(x)=\frac{-\frac{sinx}{cosx}-\frac{cosx}{cosx}}{\frac{-cosx}{cosx}+\frac{sinx}{cosx}}=\frac{-tanx-1}{-1+tanx} = \frac{1+tanx}{1-tanx}$ $\displaystyle f(x)=\frac{-\frac{sinx}{cosx}-\frac{cosx}{cosx}}{\frac{-cosx}{cosx}+\frac{sinx}{cosx}}=\frac{-tanx-1}{-1+tanx} = \frac{1+tanx}{1-tanx}$

We can then substitute the value of tanx $\displaystyle tanx$ in the obtained function.

$f(x)=\frac{1+\frac{1}{3}}{1-\frac{1}{3}}=\frac{\frac{4}{3}}{\frac{2}{3}}=2$ $\displaystyle f(x)=\frac{1+\frac{1}{3}}{1-\frac{1}{3}}=\frac{\frac{4}{3}}{\frac{2}{3}}=2$

Report an Error

Example Question #2 : Trigonometric Equations

A right triangle has an angle of $41^\circ$ $\displaystyle 41^\circ$. If the side opposite it has a length of $\displaystyle 8$, what is the hypotenuse?

Possible Answers:

10.6 $\displaystyle 10.6$

9.2 $\displaystyle 9.2$

5.25 $\displaystyle 5.25$

6.04 $\displaystyle 6.04$

12.19 $\displaystyle 12.19$

Correct answer:

12.19 $\displaystyle 12.19$

Explanation:

For this problem we will use the sine function as $\sin=\frac{O}{H}$ $\displaystyle \sin=\frac{O}{H}$.

Plug in our given information:

$\sin(41^\circ)=\frac{8}{H}$ $\displaystyle \sin(41^\circ)=\frac{8}{H}$

$H=\frac{8}{\sin(41^\circ)}$ $\displaystyle H=\frac{8}{\sin(41^\circ)}$

H=12.19 $\displaystyle H=12.19$

Report an Error

Example Question #3 : Trigonometric Equations

A right triangle has an angle of $72^\circ$ $\displaystyle 72^\circ$. If the side adjacent to it has a length of $\displaystyle 11$, what is the hypotenuse?

Possible Answers:

3.4 $\displaystyle 3.4$

3.57 $\displaystyle 3.57$

11.56 $\displaystyle 11.56$

35.6 $\displaystyle 35.6$

10.46 $\displaystyle 10.46$

Correct answer:

35.6 $\displaystyle 35.6$

Explanation:

For this problem we will use the cosine function as $\cos=\frac{A}{H}$ $\displaystyle \cos=\frac{A}{H}$.

Plug in our given information:

$\cos(72^\circ)=\frac{11}{H}$ $\displaystyle \cos(72^\circ)=\frac{11}{H}$

$H=\frac{11}{\cos(72^\circ)}$ $\displaystyle H=\frac{11}{\cos(72^\circ)}$

H=35.6 $\displaystyle H=35.6$

Report an Error

Example Question #4 : Trigonometric Equations

In a right triangle, if

$cos(x)=\frac{3}{5}$ $\displaystyle cos(x)=\frac{3}{5}$

and

$cos(y)=\frac{4}{5}$ $\displaystyle cos(y)=\frac{4}{5}$

then what does $\tan(x)$ $\displaystyle \tan(x)$ equal?

Possible Answers:

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

$\frac{4}{3}$ $\displaystyle \frac{4}{3}$

$\frac{5}{4}$ $\displaystyle \frac{5}{4}$

$\displaystyle 1$

Correct answer:

$\frac{4}{3}$ $\displaystyle \frac{4}{3}$

Explanation:

One can draw a right triangle with acute angles $\angle x$ $\displaystyle \angle x$ and $\angle y$ $\displaystyle \angle y$. The side adjacent to $\angle y$ $\displaystyle \angle y$ is 4, and the side adjacent to $\angle x$ $\displaystyle \angle x$ is 3.

$tan(x)=\frac{opposite}{adjacent}$ $\displaystyle tan(x)=\frac{opposite}{adjacent}$

Report an Error

Example Question #13 : Functions

If $sinx-cosx=\frac{1}{3}$ $\displaystyle sinx-cosx=\frac{1}{3}$ , find the value of the function $f(x)=sin^{3}x+cos^{3}x$ $\displaystyle f(x)=sin^{3}x+cos^{3}x$.

Possible Answers:

$\frac{13}{27}$ $\displaystyle \frac{13}{27}$

$-\frac{13}{27}$ $\displaystyle -\frac{13}{27}$

$\frac{11}{27}$ $\displaystyle \frac{11}{27}$

$-\frac{11}{27}$ $\displaystyle -\frac{11}{27}$

Correct answer:

$\frac{13}{27}$ $\displaystyle \frac{13}{27}$

Explanation:

We can write:

$sinx-cosx=\frac{1}{3}$ $\displaystyle sinx-cosx=\frac{1}{3}$

$\Rightarrow (sinx-cosx)^{2}=\frac{1}{9}$ $\displaystyle \Rightarrow (sinx-cosx)^{2}=\frac{1}{9}$

$\Rightarrow sin^2x+cos^2x-2sinxcosx=\frac{1}{9}$ $\displaystyle \Rightarrow sin^2x+cos^2x-2sinxcosx=\frac{1}{9}$

$\Rightarrow 2sinxcosx=1-\frac{1}{9}$ $\displaystyle \Rightarrow 2sinxcosx=1-\frac{1}{9}$

$\Rightarrow sinxcosx=\frac{4}{9}$ $\displaystyle \Rightarrow sinxcosx=\frac{4}{9}$

We can also write:

$\displaystyle (sinx-cosx)^3=sin^3x+cos^3x+3sinxcos^2x-3cosxsin^2x$

$\Rightarrow sin^3x+cos^3x=(sinx-cosx)^3+3sinxcosx(sinx-cosx)$ $\displaystyle \Rightarrow sin^3x+cos^3x=(sinx-cosx)^3+3sinxcosx(sinx-cosx)$

Now we can substitute the values of (sinx - cosx) and (sinx * cosx) in the obtained function:

$\Rightarrow sin^3x+cos^3x=(\frac{1}{3})^3+3*\frac{4}{9}*\frac{1}{3}=\frac{1}{27}+\frac{4}{9}=\frac{13}{27}$ $\displaystyle \Rightarrow sin^3x+cos^3x=(\frac{1}{3})^3+3*\frac{4}{9}*\frac{1}{3}=\frac{1}{27}+\frac{4}{9}=\frac{13}{27}$

Report an Error

View Tutors

Aaron
Certified Tutor

Tulsa Community College, Associate in Science, Mechanical Engineering.

View Tutors

Preetham
Certified Tutor

University of California-San Diego, Bachelor of Science, Structural Engineering.

View Tutors

Rishi
Certified Tutor

Hofstra University, Bachelor of Science, Biology, General.

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

MCAT Tutors in Seattle, SAT Tutors in Washington DC, GRE Tutors in Chicago, Calculus Tutors in Phoenix, GRE Tutors in Phoenix, ISEE Tutors in Chicago, MCAT Tutors in Boston, Biology Tutors in Denver, Computer Science Tutors in New York City, English Tutors in Seattle

Popular Courses & Classes

ACT Courses & Classes in Philadelphia, Spanish Courses & Classes in Seattle, SSAT Courses & Classes in Los Angeles, MCAT Courses & Classes in Denver, SSAT Courses & Classes in Denver, LSAT Courses & Classes in Houston, MCAT Courses & Classes in Phoenix, GMAT Courses & Classes in San Diego, GRE Courses & Classes in Boston, ACT Courses & Classes in Washington DC

Popular Test Prep

ISEE Test Prep in Washington DC, ISEE Test Prep in Chicago, LSAT Test Prep in Phoenix, SAT Test Prep in Seattle, MCAT Test Prep in Miami, LSAT Test Prep in Miami, SSAT Test Prep in Phoenix, LSAT Test Prep in Houston, ACT Test Prep in Atlanta, MCAT 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

High School Math : Solving Trigonometric Equations

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Trigonometric Equations

Example Question #2 : Trigonometric Equations

Example Question #3 : Trigonometric Equations

Example Question #4 : Trigonometric Equations

Example Question #13 : Functions

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: