4. Graphing Trigonometric Functions

Graph each function over a one-period interval.

y = (1/2) csc (2x + π/2)

Graph each function over a one-period interval.

y = -2 tan (¼ x)

Identify the circular function that satisfies each description.

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

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

Graph each function over a one-period interval.

y = 2 + 3 sec (2x - π)

Graph each function over a one-period interval.

y = 2 + 3 sec (2x - π)

Graph each function over a one-period interval.

y = ½ cot (4x)

Graph each function over a one-period interval.

y = ½ sec x

Graph each function over a one-period interval.

y = 1 - (1/2) csc (x - 3π/4)

Graph each function over a two-period interval.

y = tan(2x - π)

Determine an equation for each graph.

Graph each function over a two-period interval.

y = cot (3x + π/4)

Graph each function over a one-period interval.

y = -1 + csc x

Determine an equation for each graph.

Graph each function over a two-period interval.

y = 1 + tan x