Understanding Periods of Tangent and Cotangent Functions

This video tutorial covers the concepts of periodic functions, focusing on tangent and cotangent functions. It explains how to determine the period of these functions and how to graph them with various periods. The video also discusses the concept of amplitude, noting that tangent and cotangent functions do not have a defined amplitude. The tutorial includes examples of calculating periods in both radians and degrees and demonstrates graphing these functions using a graphing calculator.

What is the period of a function if it repeats every 5 units?

• 15

• 10

• 5

• 20

How do you calculate the period of y = tan(3x)?

• 3

• π

• 3π

• π/3

What is the period of y = cot(x/4) in degrees?

• 90 degrees

• 180 degrees

• 720 degrees

• 360 degrees

What is the period of y = tan(3x) in degrees?

• 60 degrees

• 45 degrees

• 30 degrees

• 90 degrees

Why do tangent and cotangent functions not have an amplitude?

• They have a fixed maximum

• They continue indefinitely

• They have a fixed minimum

• They are always zero

What is the effect of the 'A' value in the function y = 2tan(x/2)?

• Changes the period

• Horizontally compresses the graph

• Changes the amplitude

• Vertically stretches the graph

What is the period of y = tan(x/2) in radians?

• π/2

• 2π

• π

• 4π

What happens to the graph of y = 2tan(x/2) compared to the basic tangent function?

• It is compressed vertically

• It is stretched horizontally

• It is compressed horizontally

• It is stretched vertically

How is the period of y = cot(2x) different from the basic cotangent function?

• It is tripled

• It remains the same

• It is halved

• It is doubled

In the function y = 1/2 * cot(2x), what is the period?

• π

• π/2

• 4π

• 2π