4. Graphing Trigonometric Functions

Graph each function over a one-period interval.

y = 2 tan (¼ x)

In Exercises 29–44, graph two periods of the given cosecant or secant function. y = 2 sec(x + π)

Identify the circular function that satisfies each description.

period is π; function is decreasing on the interval (0, π)

In Exercises 29–44, graph two periods of the given cosecant or secant function. y = 2 sec x

Determine an equation for each graph.

In Exercises 18–24, graph two full periods of the given tangent or cotangent function. y = − 1/2 cot π/2 x

Graph each function over a two-period interval.

y = 1 - cot x

Match each function in Column I with the appropriate description in Column II.

I

y = -4 sin(3x - 2)

II

A. amplitude = 2, period = π/2, phase shift = ¾

B. amplitude = 3, period = π, phase shift = 2

C. amplitude = 4, period = 2π/3, phase shift = ⅔

D. amplitude = 2, period = 2π/3, phase shift = 4⁄3

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

y = (1/2)csc (2x - π/4)

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.)

<IMAGE>

Graph each function over a two-period interval.

y = 1 - 2 cot [2(x + π/2)]

Graph each function over a one-period interval.

y = ½ sec x

Graph each function over a two-period interval.

y= -1 + (1/2) cot (2x - 3π)

Match each function with its graph in choices A–F.

y = tan (x - π )

A. <IMAGE> B. <IMAGE> C. <IMAGE>

D. <IMAGE> E. <IMAGE> F. <IMAGE>

In Exercises 17–24, graph two periods of the given cotangent function. y = 2 cot x