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Ch. 4 - Graphs of the Circular Functions
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. 4 - Graphs of the Circular FunctionsProblema 44
Capitolo 5, Problema 44

Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts.
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Guida verificata passo dopo passo
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Identify the type of trigonometric function represented by the graph (sine or cosine) by observing where the graph starts at x = 0. If it starts at a maximum or minimum, it is likely a cosine function; if it starts at zero and goes upward, it is likely a sine function.
Determine the amplitude (a) by measuring the distance from the midline (usually y = 0) to the maximum or minimum value of the graph. The amplitude is the absolute value of this distance.
Find the period (T) of the function by measuring the length of one complete cycle on the x-axis. Use the formula for the period of sine or cosine: \(T = \frac{2\pi}{b}\), where \(b\) is the frequency parameter you need to find.
Solve for \(b\) using the period: rearrange the formula to \(b = \frac{2\pi}{T}\). Since the problem states \(b > 0\), take the positive value.
Write the equation in the form \(y = a \sin(bx)\) or \(y = a \cos(bx)\) without any phase shifts, using the values of \(a\) and \(b\) found in the previous steps.

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Basic Form of Trigonometric Functions

Trigonometric functions like sine and cosine are generally expressed as y = a sin(bx + c) + d or y = a cos(bx + c) + d, where 'a' is amplitude, 'b' affects period, 'c' is phase shift, and 'd' is vertical shift. Understanding this form helps in identifying parameters from a graph.
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Introduction to Trigonometric Functions

Amplitude and Period

Amplitude is the height from the midline to the peak of the wave, given by |a|, and period is the length of one complete cycle, calculated as 2π/b. Recognizing these from the graph allows determination of 'a' and 'b' values in the equation.
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Period of Sine and Cosine Functions

Phase Shift and Horizontal Translation

Phase shift represents horizontal shifts of the graph and is given by -c/b in the function y = a sin(bx + c). Since the question specifies no phase shifts, the equation should have c = 0, meaning the graph starts at the standard position without horizontal translation.
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Phase Shifts
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.

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Domanda del libro di testo

Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts. (Midpoints and quarter points are identified by dots.)


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Domanda del libro di testo

Graph each function over a one-period interval. See Example 3.

y = (3/2) sin [2(x + π/4)]

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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.

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686
views
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>

769
views
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.

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667
views