What are the important characteristics of the sine graph

The video tutorial covers the characteristics of sine and cosine functions, emphasizing their repetitive nature. It explains transformations of the sine function using parameters a, b, c, and d, and how these affect the graph. The tutorial defines amplitude as the half distance between the highest and lowest points on the graph and explains the period as the length it takes for the graph to repeat. The concept of X scale is introduced, highlighting its importance in plotting key points like maximum, minimum, and X intercepts. The tutorial stresses the need to understand these concepts for graphing sine and cosine functions effectively.

What is a key characteristic of both sine and cosine functions?

• They are periodic functions.

• They are linear functions.

• They are quadratic functions.

• They have a constant slope.

Which parameter in the transformation of the sine function affects vertical reflection?

• Parameter b

• Parameter c

• Parameter d

• Parameter a

How does parameter c affect the sine function?

• It shifts the graph left or right.

• It reflects the graph over the x-axis.

• It shifts the graph up or down.

• It changes the amplitude.

What is the amplitude of a sine function with a maximum point of 1 and a minimum point of -1?

• 2

• 1

• 0

• 3

How is the amplitude of a sine function determined?

• By the sum of parameters c and d

• By the absolute value of parameter a

• By the difference between maximum and minimum points

• By the absolute value of parameter b

What is the period of a standard sine function?

• 2π

• 3π

• 4π

• π

How do you calculate the period of a transformed sine function?

• 2π multiplied by b

• 2π divided by b

• π divided by a

• π multiplied by a

What is the X scale used for in graphing sine functions?

• To calculate the slope

• To determine the amplitude

• To plot important points like maxima and minima

• To find the period

How is the X scale determined for a sine function?

• By multiplying the period by 4

• By dividing the amplitude by 4

• By dividing the period by 4

• By adding the maximum and minimum points

Why is it important to find the X scale when graphing sine functions?

• To ensure the graph is linear

• To determine the function's slope

• To calculate the function's domain

• To accurately place tick marks for important points