Sine Function Properties and Graphs

The video tutorial explains how to graph the function y = 3sin(1/2x) - 2 using an interactive widget. It begins by reviewing the basic graph of y = sin(x), then explores how the graph changes with the function y = sin(1/2x), focusing on the period and amplitude. The tutorial further explains how multiplying by 3 affects the amplitude and how subtracting 2 shifts the graph vertically. The video emphasizes understanding the underlying concepts rather than just applying formulas.

What is the purpose of the interactive widget mentioned in the video?

• To solve algebraic equations

• To calculate the derivative of a function

• To find the roots of a polynomial

• To define the midline and extreme points of a function

What is the value of sin(π/2) in the basic sine function y = sin(x)?

• 1

• 0

• -1

• π

How does the coefficient 1/2 affect the period of the sine function?

• It doubles the period

• It halves the period

• It triples the period

• It has no effect on the period

What is the new period of the function y = sin(1/2x)?

• π/2

• 4π

• π

• 2π

What happens to the amplitude when the sine function is multiplied by 3?

• It becomes 1

• It becomes 3

• It becomes -3

• It becomes 0

What is the maximum value of the function y = 3sin(1/2x)?

• 3

• 2

• 4

• 1

How does subtracting 2 affect the graph of the sine function?

• It shifts the graph up by 2

• It shifts the graph down by 2

• It shifts the graph left by 2

• It shifts the graph right by 2

What is the y-value of the function y = 3sin(1/2x) - 2 when x = 0?

• -2

• 3

• 0

• 2

What remains unchanged in the function y = 3sin(1/2x) - 2?

• Amplitude

• Period

• Vertical shift

• Frequency

What is the midline of the function y = 3sin(1/2x) - 2?

• y = 3

• y = -2

• y = 1

• y = 0