Finding the Amplitude and Period of a Trigonometric Graph

The video tutorial explains how to solve the equation y = 1/2 cos(2X/3) by finding the amplitude and period. It covers the concept of amplitude, which is the absolute value of the coefficient in front of the cosine function, and how to calculate it. The tutorial also explains how to determine the period of the function using the formula 2π/B, where B is the coefficient of X. The instructor provides examples and clarifies common misconceptions, such as the correct identification of B in the equation. Additionally, the video discusses graphing and transformations, emphasizing how to adjust the graph based on translations and transformations.

What is the amplitude of the function y = 1/2 cos(2X/3)?

• 1/2

• 2

• 3

• 1

How do you determine the period of a trigonometric function?

• By adding A and B

• By finding the absolute value of A

• By using the formula 2π/B

• By multiplying A and B

In the equation y = 1/2 cos(2X/3), what is the value of B?

• 2

• 3

• 2/3

• 1/2

What is the period of the function y = 1/2 cos(2X/3)?

• 3π

• 4π

• π

• 2π

Why is it important to understand the concept of reciprocals when calculating the period?

• To determine the function's range

• To find the amplitude

• To correctly divide fractions

• To simplify the equation

What will be the focus of future lessons mentioned in the video?

• Solving quadratic equations

• Graphing and transforming trigonometric functions

• Finding the range of functions

• Calculating derivatives

How do transformations affect the graph of a trigonometric function?

• They alter the function's period

• They have no effect on the graph

• They shift and stretch the graph

• They change the function's amplitude