Transformations of Sine and Cosine Functions

This video tutorial explains how to graph sine and cosine functions with various transformations. It covers analyzing equations to identify amplitude, period, and shifts. The tutorial includes examples of graphing sine and cosine functions, demonstrating how to apply transformations step-by-step. A complex example with multiple transformations is also provided, followed by a practice problem for students.

What does the letter 'A' represent in the transformation of sine and cosine functions?

• Horizontal shift

• Period

• Vertical shift

• Amplitude

How do you calculate the period of a sine function when given the value of B?

• Subtract B from 2π

• Multiply 2π by B

• Divide 2π by B

• Add B to 2π

In the transformation of a sine function, what is the effect of a positive 'C' value?

• Shift the graph to the left

• Shift the graph downwards

• Shift the graph to the right

• Shift the graph upwards

When transforming a cosine function, what is the first step in applying a vertical shift?

• Subtract the D value from the y-coordinate

• Add the D value to the y-coordinate

• Divide the y-coordinate by the amplitude

• Multiply the y-coordinate by the amplitude

What is the amplitude of a cosine function if 'A' is -2?

• 0

• 2

• 1

• -2

In a comprehensive transformation example, what is the effect of a 'D' value of -2?

• Shift the graph to the left

• Shift the graph downwards

• Shift the graph upwards

• Shift the graph to the right

How do you handle a horizontal shift when 'C' is positive in a sine function?

• Add C to the x-coordinate

• Subtract C from the x-coordinate

• Divide the x-coordinate by C

• Multiply the x-coordinate by C

What is the new period of a sine function if B is 12?

• 2π

• 4π

• π/6

• π/12

In the final example, what is the effect of multiplying the x-coordinate by 2?

• It halves the period

• It doubles the period

• It shifts the graph to the right

• It shifts the graph to the left

What are the two changes in the practice problem at the end of the video?

• Amplitude change and horizontal shift

• Amplitude change and vertical shift

• Period change and horizontal shift

• Period change and vertical shift