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Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
Publisher: Brooks Cole
ISBN: 9781305071759

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BuyFindarrow_forward

Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
Publisher: Brooks Cole
ISBN: 9781305071759
Chapter 5.6, Problem 30E
Textbook Problem
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Amplitude, Period, Phase, and Horizontal Shift For each sine curve find the amplitude, period, phase, and horizontal shift.

30. y = 10 sin ( t π 3 )

To determine

The amplitude, period, phase and horizontal shift in simple harmonic motion.

Explanation of Solution

Given:

The displacement for the sine curve is,

y=10sin(tπ3). (1)

Formula used:

The equation for the simple harmonic motion which describes the displacement y of an object at time t is,

y=Asin(ktb) .

Where,

A is the amplitude.

b is the phase.

k is the constant.

Calculation:

The equation for the displacement in simple harmonic motion with phase difference is,

y=Asin(ktb) (2)

Compare both the equation (1) and (2),

From the equation the amplitude a is 10, the phase b is π3 and the value of k is 1

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Chapter 5 Solutions

Precalculus: Mathematics for Calculus (Standalone Book)
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Variable Stars Astronomers believe that the radius...Ch. 5.6 - Biological Clocks Circadian rhythms are biological...Ch. 5.6 - Electric Generator The armature in an electric...Ch. 5.6 - Electric Generator The graph shows an oscilloscope...Ch. 5.6 - Doppler Effect When a car with its horn blowing...Ch. 5.6 - Motion of a Building A strong gust of wind strikes...Ch. 5.6 - Shock Absorber When a car hits a certain bump on...Ch. 5.6 - Tuning Fork A tuning fork is struck and oscillates...Ch. 5.6 - Guitar String A guitar string is pulled at point P...Ch. 5.6 - Two Fans Electric fans A and B have radius 1 ft...Ch. 5.6 - Alternating Current Alternating current is...Ch. 5.6 - DISCUSS: Phases of Sine The phase of a sine curve...Ch. 5.6 - DISCUSS: Phases of the Moon During the course of a...Ch. 5 - (a) What is the unit circle, and what is the...Ch. 5 - Let t be a real number, and let P(x, y) be the...Ch. 5 - (a) Describe the steps we use to find the value of...Ch. 5 - (a) What is a periodic function? (b) What are the...Ch. 5 - (a) What is an even function, and what is an odd...Ch. 5 - (a) State the reciprocal identities. (b) Slate the...Ch. 5 - (a) Graph the sine and cosine functions. (b) What...Ch. 5 - (a) Graph the tangent and cotangent functions. (b)...Ch. 5 - (a) Graph the cosecant and secant functions. (b)...Ch. 5 - (a) Define the inverse sine function, the inverse...Ch. 5 - (a) What is simple harmonic motion? (b) What is...Ch. 5 - Suppose that an object is in simple harmonic...Ch. 5 - Consider the following models of harmonic motion....Ch. 5 - Terminal Points A point P(x, y) is given. (a) Show...Ch. 5 - Terminal Points A point P(x, y) is given. (a) Show...Ch. 5 - Reference Number and Terminal Point A real number...Ch. 5 - Reference Number and Terminal Point A real number...Ch. 5 - Reference Number and Terminal Point A real number...Ch. 5 - Reference Number and Terminal Point A real number...Ch. 5 - Values of Trigonometric Functions Find the value...Ch. 5 - Values of Trigonometric Functions Find the value...Ch. 5 - Values of Trigonometric Functions Find the value...Ch. 5 - Values of Trigonometric Functions Find the value...Ch. 5 - Values of Trigonometric Functions Find the value...Ch. 5 - Values of Trigonometric Functions Find the value...Ch. 5 - Values of Trigonometric Functions Find the value...Ch. 5 - Values of Trigonometric Functions Find the value...Ch. 5 - Values of Trigonometric Functions Find the value...Ch. 5 - Values of Trigonometric Functions Find the value...Ch. 5 - Fundamental Identities Use the fundamental...Ch. 5 - Fundamental Identities Use the fundamental...Ch. 5 - Fundamental Identities Use the fundamental...Ch. 5 - Fundamental Identities Use the fundamental...Ch. 5 - Values of Trigonometric Functions Find the values...Ch. 5 - Values of Trigonometric Functions Find the values...Ch. 5 - Values of Trigonometric Functions Find the values...Ch. 5 - Values of Trigonometric Functions Find the values...Ch. 5 - Values of Trigonometric Functions Find the values...Ch. 5 - Values of Trigonometric Functions Find the values...Ch. 5 - Values of Trigonometric Functions Find the values...Ch. 5 - Values of Trigonometric Functions Find the values...Ch. 5 - Horizontal Shifts A trigonometric function is...Ch. 5 - Horizontal Shifts A trigonometric function is...Ch. 5 - Horizontal Shifts A trigonometric function is...Ch. 5 - Horizontal Shifts A trigonometric function is...Ch. 5 - Horizontal Shifts A trigonometric function is...Ch. 5 - Horizontal Shifts A trigonometric function is...Ch. 5 - Horizontal Shifts A trigonometric function is...Ch. 5 - Horizontal Shifts A trigonometric function is...Ch. 5 - Functions from a Graph The graph of one period of...Ch. 5 - Functions from a Graph The graph of one period of...Ch. 5 - Functions from a Graph The graph of one period of...Ch. 5 - Functions from a Graph The graph of one period of...Ch. 5 - Graphing Trigonometric Functions Find the period,...Ch. 5 - Graphing Trigonometric Functions Find the period,...Ch. 5 - Graphing Trigonometric Functions Find the period,...Ch. 5 - Graphing Trigonometric Functions Find the period,...Ch. 5 - Graphing Trigonometric Functions Find the period,...Ch. 5 - Graphing Trigonometric Functions Find the period,...Ch. 5 - Graphing Trigonometric Functions Find the period,...Ch. 5 - Graphing Trigonometric Functions Find the period,...Ch. 5 - Evaluating Expressions Involving Inverse...Ch. 5 - Evaluating Expressions Involving Inverse...Ch. 5 - Evaluating Expressions Involving Inverse...Ch. 5 - Evaluating Expressions Involving Inverse...Ch. 5 - Amplitude, Period, Phase, and Horizontal Shift For...Ch. 5 - Amplitude, Period, Phase, and Horizontal Shift For...Ch. 5 - Phase and Phase Difference A pair of sine curves...Ch. 5 - Phase and Phase Difference A pair of sine curves...Ch. 5 - Even and Odd Functions A function is given. (a)...Ch. 5 - Even and Odd Functions A function is given. (a)...Ch. 5 - Even and Odd Functions A function is given. (a)...Ch. 5 - Even and Odd Functions A function is given. (a)...Ch. 5 - Even and Odd Functions A function is given. (a)...Ch. 5 - Even and Odd Functions A function is given. (a)...Ch. 5 - Sine and Cosine Curves with Variable Amplitude...Ch. 5 - Sine and Cosine Curves with Variable Amplitude...Ch. 5 - Sine and Cosine Curves with Variable Amplitude...Ch. 5 - Sine and Cosine Curves with Variable Amplitude...Ch. 5 - Maxima and Minima Find the maximum and minimum...Ch. 5 - Maxima and Minima Find the maximum and minimum...Ch. 5 - Solving Trigonometric Equations Graphically Find...Ch. 5 - Solving Trigonometric Equations Graphically Find...Ch. 5 - Discover the Period of a Trigonometric Function...Ch. 5 - Simple Harmonic Motion A point P moving in simple...Ch. 5 - Simple Harmonic Motion A mass suspended from a...Ch. 5 - Damped Harmonic Motion The top floor of a building...Ch. 5 - The point P(x, y) is on the unit circle in...Ch. 5 - The point P in the figure at the left has...Ch. 5 - Find the exact value. (a) sin76 (b) cos134 (c)...Ch. 5 - Express tan t in terms of sin t, if the terminal...Ch. 5 - If cost=817 and if the terminal point determined...Ch. 5 - A trigonometric function is given. (a) Find the...Ch. 5 - A trigonometric function is given. (a) Find the...Ch. 5 - Find the period, and graph the function. 8. y =...Ch. 5 - Find the period, and graph the function. 9....Ch. 5 - Find the exact value of each expression, if it is...Ch. 5 - The graph shown at left is one period of a...Ch. 5 - The sine curves y1=30sin(6t2) and y2=30sin(6t3)...Ch. 5 - Let f(x)=cosx1+x2. (a) Use a graphing device to...Ch. 5 - A mass suspended from a spring oscillates in...Ch. 5 - An object is moving up and down in damped harmonic...

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