Understanding Trigonometric Function Periods

The video tutorial explains how to find the period of trigonometric functions, both graphically and algebraically. It covers the concept of periods for sine and cosine functions, and how to determine the least common multiple of periods when dealing with sums or differences of these functions. Two examples are provided: one for f(x) = 2sin(x) - 1/2cos(2/3x) and another for g(x) = -3sin(4x) + 2cos(6x). The video concludes with a summary of the methods used.

What is the period of a single sine or cosine function with coefficient b?

• 2π/b

• 2π

• b

• b/2π

When analyzing the graph of f(x) = 2sin(x) - 1/2cos(2/3x), what is the period observed?

• 2π

• 3π

• 6π

• 12π

How do you find the period of a function that is a sum or difference of sine and cosine functions?

• Find the least common multiple of the periods

• Multiply the periods of each function

• Subtract the periods of each function

• Add the periods of each function

What is the period of y = 2sin(x)?

• π

• 4π

• 2π

• 3π

What is the period of y = -1/2cos(2/3x)?

• 4π

• 3π

• 6π

• 2π

In the function g(x) = -3sin(4x) + 2cos(6x), what is the period observed graphically?

• π

• 2π

• 4π

• 3π

What is the period of y = -3sin(4x)?

• π/2

• π

• 2π

• 3π

What is the period of y = 2cos(6x)?

• π/3

• π

• π/2

• 2π

How do you determine the period of g(x) = -3sin(4x) + 2cos(6x) algebraically?

• Subtract the periods of each function

• Add the periods of each function

• Multiply the periods of each function

• Find the least common multiple of the periods

What is the least common multiple of π/2 and π/3?

• π/6

• 3π

• π

• 2π