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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 8.2, Problem 26E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Evaluating Trigonometric Functions In Exercises 19-32, evaluate the six trigonometric functions of the angle without using a calculator. See Examples 2 and 3.

4 π 3

To determine

To calculate: The value of six trigonometric functions of an angle 4π3 without using a calculator.

Explanation

Given Information:

The angle is 4π3.

Formula used:

Trigonometric values of Common angles:

θ(degrees) 0° 30° 45° 60° 90° 180° 270°
θ(radians) 0 π6 π4 π3 π2 π 3π2
sinθ 0 12 22 32 1 0 −1
cosθ 1 32 22 12 0 −1 0
tanθ 0 33 1 3 Undefined 0 Undefined

Sum and difference formulas:

sin(A±B)=sinAcosB±cosAsinBcos(A±B)=cosAcosB∓sinAsinBtan(A±B)=tanA±tanB1∓tanAtanB

Calculation:

Consider the angle,

θ=4π3

Write 4π3 as π+π3. Now, evaluate the six trigonometric function as follows,

sin(4π3)=sin(π+π3)

Apply the sum rule of Sine function,

sin(π+π3)=(sinπcosπ3+cosπsinπ3)

Solve the above function using Trigonometric value,

(sinπcosπ3+cosπsinπ3)=((0)(12)+(−1)(32))=(0−32)=−32

Now, evaluate the cosine function for θ=4π3.

cos(4π3)=cos(π+π3)

Apply the sum rule of cosine function,

cos(π+π3)=(cosπcosπ3−sinπsinπ3)

Solve the above function using Trigonometric value,

(cosπcosπ3−sinπsinπ3)=((−1)(12)+(0)(32))=(−12−0)=−12

Now, evaluate the tangent function for θ=4π3

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Sect-8.1 P-1CPSect-8.1 P-2CPSect-8.1 P-3CPSect-8.1 P-4CPSect-8.1 P-1SWUSect-8.1 P-2SWUSect-8.1 P-3SWUSect-8.1 P-4SWUSect-8.1 P-5SWUSect-8.1 P-6SWU
Sect-8.1 P-7SWUSect-8.1 P-8SWUSect-8.1 P-9SWUSect-8.1 P-10SWUSect-8.1 P-1ESect-8.1 P-2ESect-8.1 P-3ESect-8.1 P-4ESect-8.1 P-5ESect-8.1 P-6ESect-8.1 P-7ESect-8.1 P-8ESect-8.1 P-9ESect-8.1 P-10ESect-8.1 P-11ESect-8.1 P-12ESect-8.1 P-13ESect-8.1 P-14ESect-8.1 P-15ESect-8.1 P-16ESect-8.1 P-17ESect-8.1 P-18ESect-8.1 P-19ESect-8.1 P-20ESect-8.1 P-21ESect-8.1 P-22ESect-8.1 P-23ESect-8.1 P-24ESect-8.1 P-25ESect-8.1 P-26ESect-8.1 P-27ESect-8.1 P-28ESect-8.1 P-29ESect-8.1 P-30ESect-8.1 P-31ESect-8.1 P-32ESect-8.1 P-33ESect-8.1 P-34ESect-8.1 P-35ESect-8.1 P-36ESect-8.1 P-37ESect-8.1 P-38ESect-8.1 P-39ESect-8.1 P-40ESect-8.1 P-41ESect-8.1 P-42ESect-8.1 P-43ESect-8.1 P-44ESect-8.1 P-45ESect-8.1 P-46ESect-8.1 P-47ESect-8.1 P-48ESect-8.1 P-49ESect-8.1 P-50ESect-8.1 P-51ESect-8.1 P-52ESect-8.1 P-53ESect-8.1 P-54ESect-8.1 P-55ESect-8.1 P-56ESect-8.1 P-57ESect-8.1 P-58ESect-8.2 P-1CPSect-8.2 P-2CPSect-8.2 P-3CPSect-8.2 P-4CPSect-8.2 P-5CPSect-8.2 P-6CPSect-8.2 P-7CPSect-8.2 P-1SWUSect-8.2 P-2SWUSect-8.2 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CONCEPT CHECK Arc Length Name a function for which the integral below represents the arc length of the function...

Calculus of a Single Variable

Given: ABDE ABDE ACDF Prove: BCFE

Elementary Geometry for College Students

In Exercises 23 - 40, determine graphically the solution set for each system of inequality and indicate whether...

Finite Mathematics for the Managerial, Life, and Social Sciences

Matching In Exercises 5-10, match the equation with its graph. [The graphs are labeled (a), (b), (c), (d), (e)....

Calculus

Finding Parallel and Perpendicular Lines In Exercises 57-62, write the general Forms of the equations of the li...

Calculus (MindTap Course List)

Finding the Angle Between Two Vectors In Exercises 1118, find the angle between the vectors (a) in radians and...

Multivariable Calculus

Which graph is best described by a linear model?

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Find for .

Study Guide for Stewart's Multivariable Calculus, 8th

A billboard is on top of a building. You are 125.0 feet from the building. You measure the angle of elevation o...

Mathematics: A Practical Odyssey

A Pew Research Center survey asked adults if their ideal place to live would have a faster pace of life or a sl...

Statistics for Business & Economics, Revised (MindTap Course List)

Explain how the enforcement of confidentiality benefits both the participants and the researcher.

Research Methods for the Behavioral Sciences (MindTap Course List)

Subtract the following expressions as indicated. (9b21)(9b21)

Mathematics For Machine Technology

Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry...

College Algebra (MindTap Course List)

In a Gallup telephone survey conducted on April 9-10,2013, the person being interviewed was asked if he would v...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Explain how inter-rater reliability is established.

Research Methods for the Behavioral Sciences (MindTap Course List)

CBS News reported that 4% of adult Americans have a food allergy (June 1, 2017, cbsnews.com/news/food-allergies...

Introduction To Statistics And Data Analysis

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