Domanda del libro di testo
Fill in the blank(s) to correctly complete each sentence.
The graph of y = sin (x + π/4) is obtained by shifting the graph of y = sin x ______ unit(s) to the ________ (right/left).
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Ch. 4 - Graphs of the Circular Functions
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 5, Problema 2
Fill in the blank(s) to correctly complete each sentence.
The graph of y = cos (x - π/6) is obtained by shifting the graph of y = cos x ______ unit(s) to the ________ (right/left).
Guida verificata passo dopo passo1
Recall that the function y = cos(x - c) represents a horizontal shift of the basic cosine graph y = cos x by c units.
If the function is y = cos(x - \(\frac{\pi}{6}\)), the graph is shifted horizontally by \(\frac{\pi}{6}\) units.
Since the expression inside the cosine is (x - \(\frac{\pi}{6}\)), this corresponds to a shift to the right by \(\frac{\pi}{6}\) units.
Therefore, the graph of y = cos(x - \(\frac{\pi}{6}\)) is obtained by shifting the graph of y = cos x \(\frac{\pi}{6}\) unit(s) to the right.
Fill in the blanks with: "\(\frac{\pi}{6}\)" and "right".
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Concetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Horizontal Phase Shift in Trigonometric Functions
A horizontal phase shift occurs when the input variable x in a trigonometric function is replaced by (x - c), shifting the graph horizontally. If the function is y = cos(x - c), the graph shifts c units to the right; if y = cos(x + c), it shifts c units to the left.
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Percorso guidato
6:31
Phase Shifts
Understanding the Argument of the Cosine Function
The argument inside the cosine function, such as (x - π/6), determines the horizontal position of the wave. Modifying this argument translates the graph along the x-axis without changing its shape or amplitude.
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Percorso guidato
5:53Graph of Sine and Cosine Function
Graphical Interpretation of Trigonometric Transformations
Graph transformations help visualize how changes in the function's formula affect its graph. Recognizing shifts, stretches, and reflections allows one to predict and sketch the new graph accurately.
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Percorso guidato
5:25Introduction to Transformations
Pratica correlata
Domanda del libro di testo
An object in simple harmonic motion has position function s(t), in inches, from an equilibrium point, as follows, where t is time in seconds.
𝒮(t) = 5 cos 2t
What is the frequency?
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Domanda del libro di testo
An object in simple harmonic motion has position function s(t), in inches, from an equilibrium point, as follows, where t is time in seconds.
𝒮(t) = 5 cos 2t
What is the amplitude of this motion?
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Domanda del libro di testo
Fill in the blank(s) to correctly complete each sentence.
The graph of y = 4 sin x is obtained by stretching the graph of y = sin x vertically by a factor of ________.
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Domanda del libro di testo
An object in simple harmonic motion has position function s(t), in inches, from an equilibrium point, as follows, where t is time in seconds.
𝒮(t) = 5 cos 2t
What is the period of this motion?
647
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