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 amplitude of a function if the coefficient of the sine function is 2?

• 1

• 2

• 3

• 4

How do you calculate the period of a trigonometric function with a coefficient of X equal to 1?

• π/2

• 2π

• π

• 4π

What is the distance between critical points if the period is 2π?

• π/4

• 2π

• π/2

• π

If a graph is shifted to the left by π units, where does the first period start?

• -π

• π

• 0

• 2π

What remains unchanged when the amplitude of a graph is increased?

• Amplitude

• Period

• Start Point

• End Point