Graphing the Sine Curve with a Period Shift

The video tutorial explains how to graph the function Y = 2 cosine of X + π by determining the amplitude and period, identifying critical points, and applying transformations. The amplitude is calculated as the absolute value of 2, and the period is 2π. Critical points are found by dividing the period by 4. The graph is then shifted and transformed, with the amplitude increased to 2 and the period remaining 2π. The tutorial concludes with a demonstration of graphing the function over one period and extending it in both directions.

What is the definition of amplitude in the context of trigonometric functions?

How do you calculate the period of a sine function?

What are critical points and how are they determined?

Explain how the amplitude and period affect the graph of a sine function.

Describe the transformations applied to the sine graph in the given context.