In Exercises 16, graph each function on the given interval. f 1t2 sin t; 32p, 6p4
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1
Infinite Geometric Series
1.1
Real Numbers, Relations, and Functions
1.2
Mathematical Patterns
1.3
Arithmetic Sequences
1.4
Lines
1.5
Linear Models
1.6
Geometric Sequences
2
Maximum Area
2.1
Solving Equations Graphically
2.2
Solving Quadratic Equations Algebraically
2.3
Applications of Equations
2.4
Other Types of Equations
2.5
Inequalities
2.5.A
Excursion: Absolute-Value Inequalities
3
Instantaneous Rates of Change
3.1
Functions
3.2
Graphs of Functions
3.3
Quadratic Functions
3.4
Graphs and Transformations
3.4.A
Excursion: Symmetry
3.5
Operations on Functions
3.5.A
Excursion: Iterations and Dynamical Systems
3.6
Inverse Functions
3.7
Rates of Change
4
Optimization Applications
4.1
Polynomial Functions
4.2
Real Zeros
4.3
Graphs of Polynomial Functions
4.3.A
Excursion: Polynomial Models
4.4
Rational Functions
4.5
Complex Numbers
4.5.A
Excursion: The Mandelbrot Set
4.6
The Fundamental Theorem of Algebra
5
Tangents to Exponential Functions
5.1
Radicals and Rational Exponents
5.2
Exponential Functions
5.3
Applications of Exponential Functions
5.4
Common and Natural Logarithmic Functions
5.5
Properties and Laws of Logarithms
5.5.A
Excursion: Logarithmic Functions to
Other Bases
5.6
Solving Exponential and Logarithmic Equations
5.7
Exponential, Logarithmic, and Other Models
6
Optimization with Trigonometry
6.1
Right-Triangle Trigonometry
6.2
Trigonometric Applications
6.3
Angles and Radian Measure
6.4
Trigonometric Functions
6.4
Review Exercises
6.5
Basic Trigonometric Identities
7
Approximations with Infinite Series
7.1
Graphs of the Sine, Cosine,
and Tangent Functions
7.2
Graphs of the Cosecant, Secant, and
Cotangent Functions
7.3
Periodic Graphs and Amplitude
7.4
Periodic Graphs and Phase Shifts
7.4.A
Excursion: Other Trigonometric Graphs
8.1
Graphical Solutions to Trigonometric Equations
8.2
Inverse Trigonometric Functions
8.3
Algebraic Solutions of Trigonometric Equations
8.4
Simple Harmonic Motion and Modeling
8.4.A
Excursion: Sound Waves
9.1
Identities and Proofs
9.2
Thomas W. Hungerford
9.2 A
Excursion: Lines and Angles
9.3
Other Identities
9.4
Using Trigonometric Identities
10.1
The Law of Cosines
10.2
The Law of Sines
10.3
The Complex Plane and Polar Form for Complex Numbers
10.4
DeMoivres Theorem and nth Roots of Complex Numbers
10.5
Vectors in the Plane
10.6
Applications of Vectors in the Plane
10.6 A
Excursion: The Dot Product
11.1
Ellipses
11.2
Analytic Geometry
11.3
Analytic Geometry
11.4
Analytic Geometry
11.4.A
Analytic Geometry
11.5
Analytic Geometry
11.6
Analytic Geometry
11.7
Analytic Geometry
11.7.A
Analytic Geometry
12.1
Systems and Matrices
12.2
Systems and Matrices
12.3
Systems and Matrices
12.4
Systems and Matrices
12.5
Systems and Matrices
12.5.A
Systems and Matrices
13.1
Basic Statistics
13.2
Measures of Center and Spread
13.3
Basic Probability
13.4
Determining Probabilities
13.4 A
Excursion: Binomial Experiments
13.5
Normal Distributions
14.1
Limits of Functions
14.2
Properties of Limits
14.2.A
Excursion: One-Sided Limits
14.3
The Formal Definition of Limit
14.4
Continuity
14.5
Limits Involving Infinity
Textbook Solutions for Precalculus
Chapter 7.1 Problem 55
Question
Fill the blanks with even or odd so that theresulting statement is true. Then prove thestatement by using an appropriate identity.Excursion 3.4.A may be helpful.a. is an ___ function.b. is an ___ function.c. is an ___ function.d. is an ___ function.e. is an ___ function.
Solution
The first step in solving 7.1 problem number 55 trying to solve the problem we have to refer to the textbook question: Fill the blanks with even or odd so that theresulting statement is true. Then prove thestatement by using an appropriate identity.Excursion 3.4.A may be helpful.a. is an ___ function.b. is an ___ function.c. is an ___ function.d. is an ___ function.e. is an ___ function.
From the textbook chapter Graphs of the Sine, Cosine,
and Tangent Functions you will find a few key concepts needed to solve this.
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full solution
full solution
Title
Precalculus 1
Author
Threasa Z. Boyer, Teresa Henry, Chris Rankin, Manda Reid
ISBN
9780030416477
Fill the blanks with even or odd so that theresulting statement is true. Then prove
Chapter 7.1 textbook questions
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Chapter 7: Problem 1 Precalculus 1
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Chapter 7: Problem 2 Precalculus 1
In Exercises 16, graph each function on the given interval. g1t2 cos t; 3p, 3p4
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Chapter 7: Problem 3 Precalculus 1
In Exercises 16, graph each function on the given interval. h1t2 tan t; 3p, 2p4
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Chapter 7: Problem 4 Precalculus 1
In Exercises 16, graph each function on the given interval. f 1t2 sin t; 35p, 3p4
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Chapter 7: Problem 5 Precalculus 1
In Exercises 16, graph each function on the given interval. g1t2 cos t; S 7p 6 , 7p 2 T
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Chapter 7: Problem 6 Precalculus 1
In Exercises 16, graph each function on the given interval. h1t2 tan t; S 5p 3 , 3pT
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Chapter 7: Problem 11 Precalculus 1
For what values of t on the interval does the graph of have vertical asymptotes?
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Chapter 7: Problem 17 Precalculus 1
For what values of t on the interval is tan t greater than 1?
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Chapter 7: Problem 18 Precalculus 1
For what values of t on the interval is tan t less than 0?
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Chapter 7: Problem 20 Precalculus 1
In Exercises 2033, find all the exact t-values for which the given statement is true.
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Chapter 7: Problem 21 Precalculus 1
In Exercises 2033, find all the exact t-values for which the given statement is true. sin t 22 2 tan t 0
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Chapter 7: Problem 22 Precalculus 1
In Exercises 2033, find all the exact t-values for which the given statement is true.
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Chapter 7: Problem 23 Precalculus 1
In Exercises 2033, find all the exact t-values for which the given statement is true. cos t 1 2 sin t 0
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Chapter 7: Problem 24 Precalculus 1
In Exercises 2033, find all the exact t-values for which the given statement is true.
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Chapter 7: Problem 25 Precalculus 1
In Exercises 2033, find all the exact t-values for which the given statement is true. 23 2 tan t 1
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Chapter 7: Problem 26 Precalculus 1
In Exercises 2033, find all the exact t-values for which the given statement is true.
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Chapter 7: Problem 27 Precalculus 1
In Exercises 2033, find all the exact t-values for which the given statement is true. cos t 23 2 cos t 0
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Chapter 7: Problem 28 Precalculus 1
In Exercises 2033, find all the exact t-values for which the given statement is true.
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Chapter 7: Problem 29 Precalculus 1
In Exercises 2033, find all the exact t-values for which the given statement is true. sin t 1 2 sin t 1
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Chapter 7: Problem 30 Precalculus 1
In Exercises 2033, find all the exact t-values for which the given statement is true.
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Chapter 7: Problem 31 Precalculus 1
In Exercises 2033, find all the exact t-values for which the given statement is true. cos t 22 2 tan t 23
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Chapter 7: Problem 32 Precalculus 1
In Exercises 2033, find all the exact t-values for which the given statement is true.
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Chapter 7: Problem 33 Precalculus 1
In Exercises 2033, find all the exact t-values for which the given statement is true. tan t 23
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Chapter 7: Problem 34 Precalculus 1
In Exercises 3443, list the transformations that change the graph of f into the graph of g. State the domain and range of g. f 1t2 cos t; g1t2 cos t 2
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Chapter 7: Problem 35 Precalculus 1
In Exercises 3443, list the transformations that change the graph of f into the graph of g. State the domain and range of g. f 1t2 cos t; g1t2 cos t
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Chapter 7: Problem 36 Precalculus 1
In Exercises 3443, list the transformations that change the graph of f into the graph of g. State the domain and range of g.f 1t2 sin t; g1t2 3 sin t
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Chapter 7: Problem 37 Precalculus 1
In Exercises 3443, list the transformations that change the graph of f into the graph of g. State the domain and range of g. f 1t2 tan t; g1t2 tan t 5
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Chapter 7: Problem 38 Precalculus 1
In Exercises 3443, list the transformations that change the graph of f into the graph of g. State the domain and range of g. f 1t2 tan t; g1t2 tan t
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Chapter 7: Problem 39 Precalculus 1
In Exercises 3443, list the transformations that change the graph of f into the graph of g. State the domain and range of g.f 1t2 cos t; g1t2 3 cos t
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Chapter 7: Problem 40 Precalculus 1
In Exercises 3443, list the transformations that change the graph of f into the graph of g. State the domain and range of g f 1t2 sin t; g1t2 2 sin t
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Chapter 7: Problem 41 Precalculus 1
In Exercises 3443, list the transformations that change the graph of f into the graph of g. State the domain and range of g.f 1t2 sin t; g1t2 3 sin t 2
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Chapter 7: Problem 42 Precalculus 1
In Exercises 3443, list the transformations that change the graph of f into the graph of g. State the domain and range of g.f 1t2 cos t; g1t2 5 cos t 3
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Chapter 7: Problem 43 Precalculus 1
In Exercises 3443, list the transformations that change the graph of f into the graph of g. State the domain and range of g.f 1t2 sin t; g1t2 sin t 3
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Chapter 7: Problem 44 Precalculus 1
In Exercises 44 48, sketch the graph of each function.
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Chapter 7: Problem 45 Precalculus 1
In Exercises 44 48, sketch the graph of each function.
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Chapter 7: Problem 46 Precalculus 1
In Exercises 44 48, sketch the graph of each function.
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Chapter 7: Problem 47 Precalculus 1
In Exercises 44 48, sketch the graph of each function. f 1t2 1 4 f 1t2 4 tan t cos t
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Chapter 7: Problem 48 Precalculus 1
In Exercises 44 48, sketch the graph of each function. f 1t2 3 sin t 1
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Chapter 7: Problem 49 Precalculus 1
In Exercises 4954, match a graph to a function. Only one graph is possible for each function.
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Chapter 7: Problem 50 Precalculus 1
In Exercises 4954, match a graph to a function. Only one graph is possible for each function. g1t2 2.5 cos t
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Chapter 7: Problem 51 Precalculus 1
In Exercises 4954, match a graph to a function. Only one graph is possible for each function.
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Chapter 7: Problem 52 Precalculus 1
In Exercises 4954, match a graph to a function. Only one graph is possible for each function. f 1t2 2.5 sin t
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Chapter 7: Problem 53 Precalculus 1
In Exercises 4954, match a graph to a function. Only one graph is possible for each function.
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Chapter 7: Problem 54 Precalculus 1
In Exercises 4954, match a graph to a function. Only one graph is possible for each function. g1t2 3 tan t 1 f 1t2 cos t 1
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Chapter 7: Problem 55 Precalculus 1
Fill the blanks with even or odd so that the resulting statement is true. Then prove the statement by using an appropriate identity. Excursion 3.4.A may be helpful. a. is an ___ function. b. is an ___ function. c. is an ___ function. d. is an ___ function. e. is an ___ function.
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Chapter 7: Problem 56 Precalculus 1
In Exercises 5659, find tan t, where the terminal side of an angle of t radians lies on the given line.
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Chapter 7: Problem 57 Precalculus 1
In Exercises 5659, find tan t, where the terminal side of an angle of t radians lies on the given line. y 1.4x
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Chapter 7: Problem 58 Precalculus 1
In Exercises 5659, find tan t, where the terminal side of an angle of t radians lies on the given line.
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Chapter 7: Problem 59 Precalculus 1
In Exercises 5659, find tan t, where the terminal side of an angle of t radians lies on the given line. y 11x
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Chapter 7: Problem 60 Precalculus 1
Scientists theorize that the average temperature at a specific location fluctuates from cooler to warmer and then to cooler again over a long period of time. The graph shows a theoretical prediction of the average summer temperature for the last 150,000 years for a location in Alaska. a. Find the highest and lowest temperature represented. b. Over what time interval does the temperature repeat the cycle? c. What is the estimated average summer temperature at the present time?
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Chapter 7: Problem 61 Precalculus 1
A rotating beacon is located at point P, 5 yards from a wall. The distance d, as measured along the wall, where the light shines is given by where t is time measured in seconds since the beacon began to rotate. When the light is aimed at point A. When the beacon is aimed to the right of A, the distance d is positive, and when it is aimed to the left of A, the value of d is negative. Graph the function and estimate the value of d for the following times. a. b. c. d. e. Determine the position of the beacon when and discuss the corresponding value of d for that value of t.
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