In Exercises, view the graphs on a calculator if the given changes are made in the indicated examples of this section.

In Example 3, change the sign before π/4.

Data from Example 3

View at least two periods of the graph of y = 2csc(2x + π/4) on a calculator. Because the period of csc x is 2π, the period of csc(2x + π/4) is 2π/2 = π. Recalling that csc x = (sin x)⁻¹, the curve will have the same displacement as y = sin(2x + π/4). Therefore, displacement is

There is some flexibility in choosing the window settings, and as an example, we choose the following settings.

Xmin = 0.5 (the displacement is π/8 = -0.4)
Xmax = 6 (displacement = −π/8; period π, −π/8 +2π = 15π/8 = 5.9)
Ymin = −6, Ymax = 6 (there is no curve between −2 and 2)

With y₁ = 2[sin(2x + π/4)]⁻¹, the function is graphed in blue in Fig. 10.29. The graph of y = 2sin(2x + π/4) is shown in red for reference.

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