Graphing Cotangent with a Phase Shift

The video tutorial explains how to graph the function y = 2 cotangent of X + π/2. It covers the concepts of amplitude and period, noting that cotangent and tangent do not have an amplitude. The period for cotangent is π/B, and the video demonstrates how to calculate the X scale and determine the start and end points for graphing. The tutorial also explains the placement of asymptotes and critical points, and how the coefficient affects the graph's shape. The video concludes with a demonstration of graphing two periods of the cotangent function.

What is the primary focus when graphing trigonometric functions like cotangent?

• Identifying the y-intercept

• Calculating the derivative

• Determining the period, amplitude, X scale, and start and end points

• Finding the maximum and minimum values

Why do cotangent and tangent functions lack an amplitude?

• Their amplitude is always zero

• They are not periodic functions

• They do not have maximum and minimum points

• They have a constant amplitude of 1

How is the period of a cotangent function determined?

• 2π divided by the coefficient of X

• π divided by the coefficient of X

• 2π times the coefficient of X

• π times the coefficient of X

What equation is used to find the start point of a cotangent function?

• Set the inside of the function equal to 2π

• Set the inside of the function equal to π

• Set the inside of the function equal to 0

• Set the inside of the function equal to -π

Where are the asymptotes placed when graphing a cotangent function?

• At the maximum and minimum points

• At the start and end points

• At the y-intercept

• At the x-intercept

How does the coefficient affect the shape of the cotangent graph?

• It changes the period of the graph

• It affects the vertical shift

• It compresses or stretches the graph horizontally

• It determines the y-intercept

What is the main characteristic of the cotangent function's graph?

• It rises to the left and falls to the right

• It rises to the right and falls to the left

• It is a vertical line

• It is a horizontal line