Skip to main content
Ch. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric Functions
Blitzer - Trigonometry 3rd Edition
Blitzer3rd EditionTrigonometryISBN: 9780137316601Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 3rd EditionCh. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric FunctionsProblema 1
Capitolo 2, Problema 1

Determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = 4 sin x

Guida verificata passo dopo passo
1
Identify the general form of the sine function, which is \(y = A \sin x\), where \(A\) represents the amplitude.
Recall that the amplitude of a sine function is the absolute value of the coefficient in front of \(\sin x\), so amplitude \(= |A|\).
In the given function \(y = 4 \sin x\), the coefficient \(A\) is 4, so the amplitude is \(|4|\).
To graph the function \(y = 4 \sin x\) along with \(y = \sin x\) on the same coordinate system for \(0 \leq x \leq 2\pi\), plot points for both functions at key values of \(x\) such as \(0\), \(\frac{\pi}{2}\), \(\pi\), \(\frac{3\pi}{2}\), and \(2\pi\).
Note that \(y = 4 \sin x\) will have peaks at \(4\) and troughs at \(-4\), while \(y = \sin x\) has peaks at \(1\) and troughs at \(-1\), so the graph of \(y = 4 \sin x\) is a vertically stretched version of \(y = \sin x\) by a factor of 4.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
4m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Amplitude of a Sine Function

The amplitude of a sine function y = a sin x is the absolute value of the coefficient a. It represents the maximum vertical distance from the midline (usually the x-axis) to the peak of the wave. For y = 4 sin x, the amplitude is 4, meaning the graph oscillates between -4 and 4.
Video consigliato:
Percorso guidato
5:05
Amplitude and Reflection of Sine and Cosine

Graphing Sine Functions

Graphing a sine function involves plotting points based on its amplitude, period, and phase shift. The basic sine curve y = sin x oscillates between -1 and 1 with a period of 2π. For y = 4 sin x, the shape is similar but scaled vertically by a factor of 4, stretching the wave.
Video consigliato:
Percorso guidato
5:53
Graph of Sine and Cosine Function

Comparing Functions on the Same Coordinate System

Plotting y = 4 sin x and y = sin x together helps visualize differences in amplitude. Both share the same period and phase but differ in vertical stretch. This comparison highlights how amplitude affects the height of the sine wave without changing its frequency or phase.
Video consigliato:
Percorso guidato
6:02
Determining Different Coordinates for the Same Point
Pratica correlata
Domanda del libro di testo

Find the exact value of each expression. sin⁻¹ 1/2

822
views
Domanda del libro di testo

Graph one period of each function. y = 3 sin 2x

749
views
Domanda del libro di testo

Graph one period of each function. y = 2 tan x/2

905
views
Domanda del libro di testo

Determine the amplitude and period of each function. Then graph one period of the function. y = 3 sin 4x

609
views
Domanda del libro di testo

Solve the right triangle shown in the figure. Round lengths to two decimal places and express angles to the nearest tenth of a degree. A = 23.5°, b = 10

604
views
Domanda del libro di testo

The graph of a tangent function is given. Select the equation for each graph from the following options: y = tan(x + π/2), y = tan(x + π), y= -tan x, y = −tan(x − π/2).

1193
views