Understanding Trigonometric Function Transformations

The video tutorial explains the transformations of trigonometric functions, focusing on the sine and cosine functions. It introduces two forms: factored and expanded, and compares them. The tutorial covers how to calculate amplitude, period, and shifts, both horizontal and vertical. An example is provided to demonstrate these concepts, followed by graphing the transformed function. The video emphasizes that both forms are useful and interchangeable, depending on the context.

What are the two forms of sine and cosine functions discussed in the video?

• Simplified and Expanded

• Factored and Expanded

• Factored and Distributed

• Simplified and Distributed

In both forms, what does the absolute value of 'a' represent?

• The phase shift

• The period

• The amplitude

• The vertical shift

How is the period of a trigonometric function determined in the factored form?

• 2π divided by the coefficient of x

• 2π divided by the constant outside the parentheses

• 2π divided by the constant factored out of the binomial

• 2π divided by the constant on the end

In the factored form, if 'd' is positive, in which direction is the function shifted?

• Left

• Down

• Right

• Up

How do you calculate the phase shift in the expanded form?

• c divided by b

• Negative c divided by b

• Negative b divided by c

• b divided by c

What is the vertical shift if 'c' is positive in the factored form?

• Shifted up

• Shifted left

• Shifted right

• Shifted down

What is the equivalent expression of 2(x - π/2) in expanded form?

• 2x + π

• 2x - π

• 2x + 2π

• 2x - 2π

What is the amplitude of the function if the absolute value of 'a' is 3?

• 1

• 2

• 3

• 4

When graphing the cosine function, what is the midline if the graph is shifted up one unit?

• y = 2

• y = 1

• y = 0

• y = -1

What is the maximum function value if the amplitude is 3 and the midline is at y = 1?

• 1

• 2

• 3

• 4