We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Evaluating Trig Functions

Study concepts, example questions & explanations for Precalculus

Create An Account

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Evaluating Trig Functions

Find the value of cot(30)+tan(30) to the nearest tenth if sin(30)=0.5 and cos(30)= 0.866 .

Possible Answers:

1.7

3.2

2.3

2.9

Correct answer:

2.3

Explanation:

Rewrite cot(30)+tan(30) in terms of sine and cosine.

$cot(30)+tan(30)=\frac{cos(30)}{sin(30)}+\frac{sin(30)}{cos(30)}$

Substitute the known values and evaluate.

$\frac{0.866}{0.5}+\frac{0.5}{0.866}=1.732+0.577367 =2.309367$

The answer to the nearest tenth is 2.3 .

Report an Error

Example Question #1 : Find The Decimal Value Of A Trigonometric Function

Determine the value of $cot(\frac{\pi}{3})$ in decimal form.

Possible Answers:

0.643

-0.156

0.577

3.125

1.732

Correct answer:

0.577

Explanation:

Ensure the calculator is in radian mode since the expression shows the angle in terms of $\pi$ . Also convert cotangent to tangent.

$cot(\frac{\pi}{3})=\frac{1}{tan(\frac{\pi}{3})}= \frac{1}{\sqrt3}=0.577$

Report an Error

Example Question #2 : Find The Decimal Value Of A Trigonometric Function

Find the decimal value of

$2\cos\left(\frac{\pi}{6}\right)$

Possible Answers:

0.866

0.3085

0.5

1.732

0.1542

Correct answer:

1.732

Explanation:

To determine the decimal value of the following trig function, $2cos(\frac{\pi}{6})$ , make sure that the calculator is in radian mode.

Compute the expression.

$2cos(\frac{\pi}{6})=2(0.866)=1.732$

Report an Error

Example Question #2 : Find The Decimal Value Of A Trigonometric Function

Determine the correct value of

$sin\left(\frac{1}{2}^{\circ}\right)$ .

Possible Answers:

2.62

1.05

0.48

0.009

1.57

Correct answer:

0.009

Explanation:

The question $sin(\frac{1}{2})$ asks for the y-coordinate on the unit circle when the degree angle is $\frac{1}{2}$ .

Be careful not to confuse finding the value of the angle when the y-value of the coordinate of the unit circle is $\frac{1}{2}$ .

Ensure that the calculator is in degree mode.

$sin(\frac{1}{2})=0.00872=0.009$

Report an Error

Example Question #1 : Evaluating Trig Functions

Find the value of

$\sin(270^\circ)+\cos(60^\circ)$ .

Possible Answers:

-1.13

1.5

0.5

-0.5

1.13

Correct answer:

-0.5

Explanation:

Before beginning this problem on a calculator, though this is not necessary since these are special angles, ensure that the mode of the calculator is in degrees.

Input the values of the expression and solve.

sin(270)+cos(60)= -1+0.5 = -0.5

Report an Error

Example Question #2 : Evaluating Trig Functions

Solve for all x on the interval $0^{\circ} \leq x \leq 360^{\circ}$

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

Possible Answers:

$90^{\circ}$ , $135^{\circ}$

$45^{\circ}$ , $90^{\circ}$

$45^{\circ}$ , $135^{\circ}$

$135^{\circ}$ , $225^{\circ}$

Correct answer:

$45^{\circ}$ , $135^{\circ}$

Explanation:

Solve for all x on the interval $0^{\circ} \leq x \leq 360^{\circ}$

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

We can begin by recalling which two quadrants have a positive sine. Because sine corresponds to the y-value, we know that sine is positive in quadrants I and II.

Next, recall where we get $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2}}{2}$ always corresponds to our $45^{\circ}$ -increment angles. In this case, the angles we are looking for are $45^{\circ}$ and $135^{\circ}$ , because those are the two $45^{\circ}$ -increment angles in the first two quadrants.

Now, you might be saying, "what about $90^{\circ}$ ? That is an increment of 45."

While that is true, $sin(90^{\circ})=1$ , not $\frac{\sqrt{2}}{2}$

So our answer is:

$45^{\circ}$ , $135^{\circ}$

Report an Error

Example Question #3 : Evaluating Trig Functions

Solve for all x on the interval $0^{\circ}\leq x \leq 90^{\circ}$

tan(x)=1

Possible Answers:

$45^{\circ}$

$30^{\circ}$

$0^{\circ}$

$90^{\circ}$

Correct answer:

$45^{\circ}$

Explanation:

Solve for all x on the interval $0^{\circ}\leq x \leq 90^{\circ}$

tan(x)=1

Remember Soh, Cah, Toa?

For this problem it helps to recall that $Tangent=\frac{opposite}{adjacent}$

Since our tangent is equal to 1 in this problem, we know that our opposite and adjacent sides must be the same (otherwise we wouldn't get "1" when we divided them)

Can you think of any angles in the first quadrant which yield equal x and y values?

If you guessed $45^{\circ}$ you guessed right! Remember that your $45^{\circ}$ angle in the unit circle will give you a 45/45/90 triangle, which will have equal height and base.

Report an Error

Example Question #1 : Evaluating Trig Functions

Q3 new

The above triangle is a right triangle. Find the value of $\theta$ (in degrees).

Possible Answers:

$57^\circ$

$33^\circ$

$65^\circ$

$28^\circ$

$49^\circ$

Correct answer:

$57^\circ$

Explanation:

One can setup the relationship

$cos(\theta)=\frac{adjacent}{hypotenuse}$

$cos(\theta)=\frac{6}{11}$ .

After taking the arccosine,

$cos^{-1}(cos(\theta))=cos^{-1}\left(\frac{6}{11} \right )$

the arccosine cancels out the cosine leaving just the value of $\theta$ .

$\\ \theta=cos^{-1}\left(\frac{6}{11} \right ) \\ \theta= 56.944^\circ \\ \theta= 57^\circ$

Report an Error

Example Question #1 : Find The Degree Measure Of An Angle For Which The Value Of A Trigonometric Function Is Known

What is the value of $\theta$ (in degrees)?

Possible Answers:

$57^\circ$

$61^\circ$

$42^\circ$

$70^\circ$

$26^\circ$

Correct answer:

$61^\circ$

Explanation:

One can setup the relationship

$\\tan(\theta) = \frac{opposite}{adjacent}\\ tan(\theta)=\frac{9}{5}$ .

After taking the arctangent,

$tan^{-1}(tan(\theta))=tan^{-1}\left(\frac{9}{5}\right)$

the arctangent cancels out the tangent and we are left with the value of $\theta$ .

$\\ \theta=tan^{-1}\left(\frac{9}{5} \right ) \\ \theta=60.945^\circ \\ \theta=61^\circ$

Report an Error

Example Question #2 : Find The Degree Measure Of An Angle For Which The Value Of A Trigonometric Function Is Known

Solve for $\theta$ :

$\sin(3\theta) = -\frac{\sqrt{3}}{2}$

Possible Answers:

$\frac{ \pi }{9}$ or $\frac{2 \pi }{9}$

$\frac{5 \pi }{9}$ or $\frac{\pi }{9 }$

$\frac{5 \pi }{9}$ or $\frac{4 \pi }{9 }$

$5 \pi$ or $4 \pi$

$\frac{4 \pi}{3}$ or $\frac{5 \pi }{3 }$

Correct answer:

$\frac{5 \pi }{9}$ or $\frac{4 \pi }{9 }$

Explanation:

If the sine of an angle, in this case $3 \theta$ is $-\frac{ \sqrt 3 }{2}$ , the angle must be $\frac{4 \pi }{3}$ or $\frac{5 \pi }{3 }$ .

Then we need to solve for theta by dividing by 3:

$\frac{4 \pi }{3} \div 3 = \frac{4 \pi }{3} \cdot \frac{1}{3} = \frac{4 \pi }{9 }$

$\frac{5 \pi }{3} \div 3 = \frac{5 \pi }{3} \cdot \frac{1}{3} = \frac{5 \pi }{9 }$

Report an Error

View Pre-Calculus Tutors

Zara
Certified Tutor

University of Manitoba, Bachelor in Arts, Mathematics.

View Pre-Calculus Tutors

James
Certified Tutor

University of Georgia, Bachelor in Arts, Political Science and Government.

View Pre-Calculus Tutors

Bhupinder
Certified Tutor

Panjab University, Bachelor of Engineering, Biotechnology. Hamburg University of Technology, Master of Science, Chemical Engi...

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Algebra Tutors in Dallas Fort Worth, Algebra Tutors in Chicago, SAT Tutors in Philadelphia, Calculus Tutors in New York City, MCAT Tutors in San Francisco-Bay Area, Reading Tutors in Houston, Biology Tutors in Seattle, Algebra Tutors in Philadelphia, ISEE Tutors in Los Angeles, GMAT Tutors in Boston

Popular Courses & Classes

LSAT Courses & Classes in Chicago, ISEE Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Seattle, GRE Courses & Classes in Denver, GRE Courses & Classes in Philadelphia, ISEE Courses & Classes in New York City, ISEE Courses & Classes in Washington DC, MCAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Los Angeles

Popular Test Prep

ISEE Test Prep in Dallas Fort Worth, MCAT Test Prep in Dallas Fort Worth, SSAT Test Prep in Seattle, ACT Test Prep in Phoenix, ISEE Test Prep in Phoenix, LSAT Test Prep in Chicago, ISEE Test Prep in Houston, ISEE Test Prep in Washington DC, GMAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Seattle

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

Precalculus : Evaluating Trig Functions

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Evaluating Trig Functions

Example Question #1 : Find The Decimal Value Of A Trigonometric Function

Example Question #2 : Find The Decimal Value Of A Trigonometric Function

Example Question #2 : Find The Decimal Value Of A Trigonometric Function

Example Question #1 : Evaluating Trig Functions

Example Question #2 : Evaluating Trig Functions

Example Question #3 : Evaluating Trig Functions

Example Question #1 : Evaluating Trig Functions

Example Question #1 : Find The Degree Measure Of An Angle For Which The Value Of A Trigonometric Function Is Known

Example Question #2 : Find The Degree Measure Of An Angle For Which The Value Of A Trigonometric Function Is Known

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: