Exploring Sine and Cosine Graph Transformations

The video tutorial explores how the parameters a, b, c, and d affect the graph of the sine function y = a * sin(b(x - c)) + d. It explains that 'a' determines the amplitude and reflection, 'b' affects the period and reflection, 'c' causes horizontal shifts, and 'd' results in vertical shifts. The tutorial uses Desmos to visualize these transformations, demonstrating how changes in each parameter alter the graph's appearance.

What tool is used in this lesson to explore the effects of parameters on the sine graph?

• GeoGebra

• Desmos

• Wolfram Alpha

• GraphCalc

What does the absolute value of 'a' represent in the sine function?

• Period

• Phase Shift

• Amplitude

• Vertical Shift

How is the period of the sine function calculated in radians?

• 2π * |b|

• 2π / |b|

• 360° * |b|

• 360° / |b|

What happens to the sine graph when 'a' is negative?

• It stretches vertically

• It reflects across the midline

• It shifts down

• It shifts up

If 'a' is between -1 and 1, what happens to the graph?

• It is horizontally compressed

• It is horizontally stretched

• It is vertically compressed

• It is vertically stretched

What effect does increasing 'b' have on the sine graph?

• Shifts the graph right

• Increases the period

• Decreases the period

• Shifts the graph left

How does a positive 'c' value affect the sine graph?

• Increases the amplitude

• Decreases the amplitude

• Shifts the graph left

• Shifts the graph right

What is the midline of the sine function when 'd' is involved?

• y = c

• y = d

• y = b

• y = a

What happens to the graph when 'd' is negative?

• It reflects across the x-axis

• It shifts down

• It shifts up

• It reflects across the y-axis

Which parameter affects the horizontal shift of the sine graph?

• c

• b

• a

• d