Domanda del libro di testo
Determine an equation for each graph.
625
views
Ch. 4 - Graphs of the Circular Functions
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
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 4
Fill in the blank(s) to correctly complete each sentence.
The graph of y = -3 sin x is obtained by stretching the graph of y = sin x by a factor of ________ and reflecting across the ________-axis.
Guida verificata passo dopo passo1
Identify the general form of the sine function transformation: \(y = A \sin x\), where \(A\) represents the amplitude, which affects the vertical stretch or compression of the graph.
Compare the given function \(y = -3 \sin x\) with the basic sine function \(y = \sin x\). Notice that the amplitude changes from 1 to 3, indicating a vertical stretch by a factor of 3.
Observe the negative sign in front of the amplitude, which means the graph is reflected across the x-axis.
Summarize the transformation: the graph is stretched vertically by a factor of 3 and reflected across the x-axis.
Fill in the blanks accordingly: The graph of \(y = -3 \sin x\) is obtained by stretching the graph of \(y = \sin x\) by a factor of 3 and reflecting across the x-axis.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Concetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Amplitude and Vertical Stretching
The amplitude of a sine function is the absolute value of the coefficient before sin x, which determines the vertical stretch or compression. For y = -3 sin x, the amplitude is 3, meaning the graph is stretched vertically by a factor of 3 compared to y = sin x.
Video consigliato:
Percorso guidato
6:02
Stretches and Shrinks of Functions
Reflection Across the x-axis
A negative coefficient before the sine function indicates a reflection of the graph across the x-axis. This flips the graph upside down, changing the direction of the peaks and troughs while preserving the shape.
Video consigliato:
Percorso guidato
5:00Reflections of Functions
Basic Sine Function Graph
The graph of y = sin x is a periodic wave oscillating between -1 and 1 with a period of 2π. Understanding this baseline graph is essential to recognize how transformations like stretching and reflection affect its shape.
Video consigliato:
Percorso guidato
5:53Graph of Sine and Cosine Function
Pratica correlata
Domanda del libro di testo
Determine an equation of the form y = a cos bx or y = a sin bx, where b > 0, for the given graph. See Example 6.
<IMAGE>
1189
views
Domanda del libro di testo
Fill in the blank(s) to correctly complete each sentence.
The graph of y = 6 + 3 sin x is obtained by shifting the graph of y = 3 sin x ________ unit(s) __________ (up/down).
711
views
Domanda del libro di testo
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 2 sin 2x
582
views
Domanda del libro di testo
Determine an equation for each graph.
630
views
Domanda del libro di testo
Fill in the blank(s) to correctly complete each sentence.
The graph of y = -5 + 2 cos x is obtained by shifting the graph of y = 2 cos x ________ unit(s) __________ (up/down).
639
views