Understanding Periodic Functions and Their Properties

The video tutorial from V Academy covers the concept of periodicity in trigonometric functions. It begins with defining periodic functions and explaining the significance of the period. The tutorial then discusses the periods of basic trigonometric functions like sine, cosine, and tangent. It further explains how to calculate the period for functions in the form of f(ax + b) and provides examples to illustrate these calculations. The video concludes with a summary of the key concepts discussed.

What is the definition of a periodic function?

• A function that never repeats its values.

• A function that repeats its values at regular intervals.

• A function that is always increasing.

• A function that is always decreasing.

What is the period of the function sin(x)?

• π

• 2π

• π/2

• 4π

What is the period of the function cos(x)?

• π

• 2π

• π/2

• 4π

What is the period of the function tan(x)?

• π/2

• 2π

• 4π

• π

How is the period of f(ax + b) related to the period of f(x)?

• It is the period of f(x) divided by |a|.

• It is the same as the period of f(x).

• It is the period of f(x) multiplied by |a|.

• It is the period of f(x) plus |a|.

What is the period of sin(ax + b)?

• π

• 2π/|a|

• π/|a|

• 2π

What is the period of cos(ax + b)?

• 2π

• π

• 2π/|a|

• π/|a|

What is the period of tan(ax + b)?

• 2π

• π

• π/|a|

• 2π/|a|

In the example of cos(2x/3), what is the value of 'a'?

• 1/3

• 3

• 3/2

• 2/3

What is the period of cos(2x/3)?

• 2π

• π

• 4π

• 3π