4. Graphing Trigonometric Functions

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

Determine an equation for each graph.

Graph each function over a two-period interval.

y = 1 - cot x

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

The tangent and secant functions are undefined for the same values.

Graph each function over a two-period interval.

y = -1 + 2 tan x

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.

y= -1 + (1/2) cot (2x - 3π)

Graph each function over a two-period interval.

y = 1 - 2 cot [2(x + π/2)]

Consider the function g(x) = -2 csc (4x + π). What is the domain of g? What is its range?

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.)

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A rotating beacon is located at point A, 4 m from a wall. The distance a is given by

a = 4 |sec 2πt|,

where t is time in seconds since the beacon started rotating. Find the value of a for each time t. Round to the nearest tenth if applicable.

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t = 1.24

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.)

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