4. Graphing Trigonometric Functions

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

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>

Below is a graph of the function $y=\(\tan\]\left\)(bx\(\right\))$. Determine the value of b.

Below is a graph of the function $y=\(\cot\[\left\)(bx+\(\frac{\pi}{2}\]\right\))$. Determine the value of b.

Graph each function over a one-period interval.

y = 3 sec [(1/4)x]

Graph each function over a one-period interval.

y = - (1/2) csc (x + π/2)

Graph each function over a one-period interval. See Examples 1–3.

y = tan 4x

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

y = (1/2)csc (2x - π/4)

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

y = 2 sec(πx - 2π)

Graph each function over a one-period interval.

y = csc (x - π/4)

Graph each function over a one-period interval. See Examples 1–3.

y = 2 tan x

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

y = 1/3 tan (3x - π/3)

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

y = cot (x/2 + 3π/4)

Graph each function over a one-period interval.

y = sec (x + π/4)

Graph each function over a one-period interval.

y = 2 tan (¼ x)