Exploring Transformations of Sine and Cosine Functions

This lesson uses Desmos to explore transformations of the sine and cosine functions. It covers how parameters a, b, c, and d affect the graph, including amplitude, period, phase shift, and vertical shift. The video demonstrates graphing the basic sine function and shows how changes in each parameter alter the graph's appearance.

What is the amplitude of the function y = a * sin(bx - c) + d?

• The absolute value of 'c'

• The absolute value of 'd'

• The absolute value of 'b'

• The absolute value of 'a'

If 'a' is negative, what transformation occurs to the sine graph?

• It shifts up

• It stretches horizontally

• It reflects across the midline

• It compresses vertically

How does increasing the value of 'b' affect the period of the sine function?

• The period decreases

• The period becomes undefined

• The period remains the same

• The period increases

What happens to the graph when 'b' is between -1 and 1?

• The graph is vertically stretched

• The graph is horizontally stretched

• The graph is horizontally compressed

• The graph is vertically compressed

What is the phase shift of the function y = a * sin(bx - c) + d?

• c divided by b

• b

• c

• b divided by c

If 'c' is positive, in which direction does the graph shift?

• Up

• Right

• Left

• Down

What is the midline of the function y = a * sin(bx - c) + d?

• y = b

• y = a

• y = c

• y = d

How does a positive 'd' value affect the graph?

• Reflects the graph

• Shifts the graph up

• Compresses the graph

• Shifts the graph down

What transformation occurs when 'd' is negative?

• The graph reflects across the x-axis

• The graph shifts down

• The graph shifts up

• The graph stretches vertically

Which of the following is NOT a transformation discussed in the video?

• Amplitude

• Period

• Phase Shift

• Frequency