Understanding Sine and Cosine Functions

The video tutorial explains how to determine the equations of sine and cosine functions from graphs. It covers the non-uniqueness of these equations and provides step-by-step examples for both sine and cosine functions. Key concepts such as amplitude, period, phase shift, and vertical shift are discussed, with practical examples to illustrate the process of deriving the equations.

What is a key challenge in finding the equation of a sine or cosine graph?

• The equations are always linear.

• The equations are always unique.

• The equations are always quadratic.

• The equations are not unique.

What is the first step in determining the equation of a sine function from a graph?

• Calculate the derivative of the graph.

• Highlight one period of the graph.

• Find the maximum point of the graph.

• Determine the x-intercepts of the graph.

How is the amplitude of a sine function determined from a graph?

• By finding the distance from the center line to the maximum.

• By finding the distance between two peaks.

• By calculating the area under the curve.

• By measuring the width of the graph.

What does a vertical shift in a sine function indicate?

• A change in the amplitude.

• A shift along the x-axis.

• A shift along the y-axis.

• A change in the period.

In the second example, what is the vertical shift of the sine function?

• Down 1

• Down 2

• Up 1

• Up 2

What is the period of the sine function in the second example?

• Pi/2

• 3Pi/2

• Pi

• 2Pi

What is the phase shift of the cosine function in the third example?

• Right Pi/4

• Right Pi/2

• Left Pi/4

• Left Pi/2

How is the cosine function in the third example different from the typical cosine function?

• It has no phase shift.

• It has no vertical shift.

• It starts at a minimum.

• It starts at a maximum.

What is the amplitude of the cosine function in the third example?

• 2

• 1

• -2

• 3

What is emphasized about the equations of sine and cosine functions in the conclusion?

• They are always quadratic.

• They are always linear.

• They can be found using different graph segments.

• They are always unique.