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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 4.42
Capitolo 5, Problema 4.42

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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Guida verificata passo dopo passo
1
Identify the type of trigonometric function: Determine whether the graph resembles a sine or cosine function based on its shape and starting point.
Determine the amplitude 'a': Measure the vertical distance from the midline of the graph to a peak or trough. This value is the amplitude.
Determine the period of the function: Measure the horizontal distance required for the graph to complete one full cycle.
Calculate the value of 'b': Use the formula for the period of a sine or cosine function, which is \( \frac{2\pi}{b} \), and solve for 'b'.
Write the equation: Substitute the values of 'a' and 'b' into the form \( y = a \cos(bx) \) or \( y = a \sin(bx) \), depending on the function type identified in step 1.

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Amplitude

Amplitude refers to the maximum height of a wave from its central axis. In the equations y = a cos(bx) or y = a sin(bx), the value 'a' represents the amplitude. It determines how far the graph stretches vertically from the midline, affecting the overall height of the peaks and depth of the troughs.
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Amplitude and Reflection of Sine and Cosine

Period

The period of a trigonometric function is the distance along the x-axis required for the function to complete one full cycle. In the equations y = a cos(bx) or y = a sin(bx), the period is calculated as 2π/b. This concept is crucial for understanding how frequently the wave oscillates and is essential for matching the graph to the correct function.
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Period of Sine and Cosine Functions

Phase Shift

Phase shift refers to the horizontal displacement of a trigonometric graph. It occurs when the function is adjusted by adding or subtracting a constant inside the argument of the sine or cosine function. Understanding phase shift is important for accurately positioning the graph along the x-axis, which can be necessary to match the given graph in the problem.
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Phase Shifts
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