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

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Chapter 8.2, Problem 23E
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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.

2 π 3

To determine

To calculate: The value of six trigonometric functions of an angle 2π3 without using a calculator.

Explanation

Given Information:

The angle is 2π3.

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

The formulas for negative angles are,

sin(−θ)=−sin(θ)cos(−θ)=cos(θ)

The formula for double angles,

sin(θ)=2sin(θ)cos(θ)cos(θ)=2cos2(θ)−1tan(θ)=sin(θ)cos(θ)

Calculation:

Consider the angle,

θ=2π3

Now, evaluate the value of six trigonometric functions for θ=2π3 using Trigonometric values of common angles.

sin(2π3)=2sin(π3)cos(π3)=2(32)(12)=(32)

Next,

cos(2π3)=2cos2(π3)−1=2(14)−1=−12

Next,

tan(2π3)=sin(2π3)cos(2π3)=−3

Evaluate the csc(2π3) using reciprocal identities

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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
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In Exercises 9 to 28, use the drawings as needed to answer the following questions. How many lines can be drawn...

Elementary Geometry for College Students

Show that the linear programming problem Maximize P=2x+2y4z subject to 3x+3y2z100 5x+5y+3z150 x0,y0,z0 has infi...

Finite Mathematics for the Managerial, Life, and Social Sciences

Finding VolumeIn Exercises 1720, use a double integral to find the volume of the indicated solid.

Multivariable Calculus

A bacteria culture starts with 50 organisms and after 2 hours there are 100. Assuming natural growth, how many ...

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

converges to: 2 the series diverges

Study Guide for Stewart's Multivariable Calculus, 8th

Proof For a smooth curve given by the parametric equations x=f(t)andy=g(t), prove that the curvature is given b...

Calculus

Finding the Least Squares Regression QuadraticIn Exercises 3336, use the result of Exercise 31 to find the leas...

Calculus (MindTap Course List)

Explain how a matched-subjects design attempts to avoid the major problem with between-subjects experiments (in...

Research Methods for the Behavioral Sciences (MindTap Course List)

Playbill magazine reported that the mean annual household income of its readers is 119,155 (Playbill, January 2...

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

This exercise requires use of a statistical software package. Using a statistical computer package, compare the...

Introduction To Statistics And Data Analysis

Practice Evaluate each expression. 18!6!(186)!

College Algebra (MindTap Course List)

The following formulas are used in the machine trades. Substitute the given values in each formula and solve fo...

Mathematics For Machine Technology

Marvel Studios motion picture Guardians of the Galaxy opened over the first two days of the 2014 Labor Day week...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Explain how the terms quasi-independent variable and dependent variable are used in nonexperimental, quasi-expe...

Research Methods for the Behavioral Sciences (MindTap Course List)

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