In Exercises, graph the function if the given changes are made in the indicated examples of this section.

In Example 4, if the sign before π/6 is changed, sketch the graph of the resulting function.

Data from Example 4

View the graph of y = 2 cos(1/2x − π/6 on a calculator. From the values a = 2, b = 1 2, and c = −π/6, we determine that

1. The amplitude is 2
2. The period is 2π ÷ 1/2 = 4π.

3. The displacement is −(−π/6) ÷ 1/2 = π/3

This curve’s cycle starts at x = π/3 (≈1.05) and ends at π/3 + 4π = 13π/3 

(≈13.6). When choosing the window settings, we should make sure these two values are between the Xmin and Xmax. The amplitude determines the Ymin and Ymax. The graph is shown in Fig. 10.18.

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NORMAL FLOAT AUTO REAL RADIAN MP M 14 -1 Fig. 10.18 0