4. Graphing Trigonometric Functions

Each function graphed is of the form y = c + cos x, y = c + sin x, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine an equation of the graph.

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Each function graphed is of the form y = c + cos x, y = c + sin x, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine an equation of the graph.

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Graph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.

y = 2 sin ¼ x

Each function graphed is of the form y = c + cos x, y = c + sin x, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine an equation of the graph.

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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 ________.

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = 2 sin (x + π)

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = -¼ cos (½ x + π/2)

Decide whether each statement is true or false. If false, explain why.

The graph of y = sec x in Figure 37 suggests that sec(-x) = sec x for all x in the domain of sec x.

Graph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.

y = -2 sin 2 πx

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = 3 cos [π/2 (x - ½)]

Graph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.

y = ½ cos π x

2

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = 2 - sin(3x - π/5)

Graph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.

y = π sin πx

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.

Graph each function over a one-period interval.

y = -½ cos (πx - π)