4. Graphing Trigonometric Functions

In Exercises 17–24, graph two periods of the given cotangent function. y = 1/2 cot 2x

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 = cot (x/2 + 3π/4)

Determine an equation for each graph.

In Exercises 29–44, graph two periods of the given cosecant or secant function. y = −1/2 sec πx

In Exercises 45–52, graph two periods of each function. y = csc|x|

Graph each function over a one-period interval.

y = cot (3x)

Graph each function over a two-period interval.

y = tan(2x - π)

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

y = 2 tan x

In Exercises 45–52, graph two periods of each function. y = sec(2x + π/2) − 1

Consider the following function from Example 5. Work these exercises in order.

y = -2 - cot (x - π/4)

Use the fact that the period of this function is π to find the next positive x-intercept. Round to the nearest hundredth.

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

y = tan 3x

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

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.

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