Transformations of Sine and Cosine Functions

The video tutorial covers the properties and characteristics of sine and cosine graphs, including their bounded nature, range, and domain. It explains how transformations affect these graphs, focusing on amplitude, period, and frequency. The tutorial provides formulas for graphing sine and cosine functions and discusses how to determine amplitude and period. It also highlights the impact of transformations on graph cycles and the role of frequency in graph analysis.

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

• They only increase.

• They have a maximum and minimum value.

• They are unbounded.

• They only decrease.

What is the general form of a sine function with transformations?

• y = a * sin(BX + C) + D

• y = a * sin(BX) - C + D

• y = a * sin(BX) + C + D

• y = a * sin(BX - C) + D

What is the effect of 'C' on the graph?

• It shifts the graph vertically

• It shifts the graph horizontally

• It compresses the graph horizontally

• It stretches the graph vertically

What is the effect of 'D' on the graph?

• It shifts the graph horizontally

• It shifts the graph vertically

• It compresses the graph horizontally

• It stretches the graph vertically

What is the effect of transformations on the parent function?

• They have no effect

• They change the range and domain

• They change the amplitude and period

• They change the frequency and phase shift

What is the range of the parent sine and cosine functions?

• -2 to 2

• 0 to 2

• -1 to 1

• 0 to 1

What is the domain of the parent sine and cosine functions?

• 0 to infinity

• 0 to 1

• -1 to 1

• -infinity to infinity

What is the range of a transformed sine or cosine function?

• Depends on the values of A and D

• Always -1 to 1

• Always 0 to 1

• Depends on the values of B and C

What is the domain of a transformed sine or cosine function?

• Depends on the values of A and D

• Always -infinity to infinity

• Depends on the values of B and C

• Always 0 to infinity

How is the amplitude of a sine or cosine graph determined?

• By the value of B

• By the value of C

• By the absolute value of A

• By the value of D