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Ch. 1 - Functions
Briggs - Calculus: Early Transcendentals 3rd Edition
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Not the one you use?Change textbook
All textbooksBriggs 3rd EditionCh. 1 - FunctionsProblem 66
Chapter 1, Problem 66

Find a trigonometric function ff represented by the graph in the figure. <IMAGE>

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1
Identify the key features of the trigonometric graph, such as amplitude, period, phase shift, and vertical shift. These features will help determine the specific trigonometric function.
Determine the amplitude by measuring the vertical distance from the midline of the graph to a peak or trough. The amplitude is the absolute value of this distance.
Calculate the period of the function by identifying the horizontal length of one complete cycle of the graph. This can be done by measuring the distance between two consecutive peaks or troughs.
Check for any phase shift by observing if the graph is shifted horizontally from the standard position of a basic trigonometric function like sine or cosine.
Look for any vertical shift by determining if the midline of the graph is above or below the x-axis. This will indicate if the function has been shifted up or down.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Trigonometric Functions

Trigonometric functions, such as sine, cosine, and tangent, relate angles to the ratios of sides in right triangles. They are periodic functions, meaning they repeat their values in regular intervals, which is crucial for analyzing wave-like behaviors in graphs. Understanding these functions is essential for interpreting the graph and identifying the specific function that matches its shape.
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Introduction to Trigonometric Functions

Graph Interpretation

Graph interpretation involves analyzing the visual representation of a function to extract information about its behavior, such as amplitude, period, and phase shift. For trigonometric functions, recognizing key features like peaks, troughs, and intercepts helps in determining the specific function that corresponds to the graph. This skill is vital for solving problems that require matching a function to its graphical representation.
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Graphing The Derivative

Function Representation

Function representation refers to expressing a mathematical relationship in various forms, such as equations, graphs, or tables. In the context of trigonometric functions, this includes writing the function in standard form, which may involve parameters like amplitude and frequency. Understanding how to convert between these representations is crucial for accurately identifying the function depicted in the graph.
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Properties of Functions
Related Practice
Textbook Question

{Use of Tech} Height and time The height in feet of a baseball hit straight up from the ground with an initial velocity of 64 ft/s is given by h= ƒ(t) = 64t - 16t²  where t is measured in seconds after the hit.


e. At what time is the ball at a height of 10 ft on the way down? 

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Textbook Question

Prove the following identities.

secθ=1cosθ\(\sec\]\theta\)=\(\frac{1}{\cos\theta}\)

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Textbook Question

Prove the following identities.

tanθ=sinθcosθ\(\tan\]\theta\)=\(\frac{\sin\theta}{\cos\theta}\)

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Textbook Question

{Use of Tech} Height and time The height in feet of a baseball hit straight up from the ground with an initial velocity of 64 ft/s is given by h= ƒ(t) = 64t - 16t²  where t is measured in seconds after the hit.


d. At what time is the ball at a height of 30 ft on the way up?

257
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Textbook Question

{Use of Tech} Height and time The height in feet of a baseball hit straight up from the ground with an initial velocity of 64 ft/s is given by h= ƒ(t) = 64t - 16t²  where t is measured in seconds after the hit.


c. Find the inverse function that gives the time t at which the ball is at height h as the ball travels downward. Express your answer in the form t = ƒ⁻¹ (h)

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Textbook Question

Changing bases Convert the following expressions to the indicated base.


ln∣x∣\(\ln\]\left\)|x\(\right\)| using base 5

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