Understanding Sine and Cosine Functions

The video tutorial covers the graphs of sine and cosine functions, explaining their periodic nature and how constants like amplitude and vertical shift affect their range. It demonstrates graphing techniques using the unit circle and explores complex graphing examples with phase shifts. The tutorial also discusses determining function properties such as amplitude, midline, and period, and uses graphing calculators to visualize functions.

Why are sine and cosine functions called periodic?

• Because they have a constant slope

• Because they repeat their values at regular intervals

• Because they are always decreasing

• Because they are always increasing

What is the period of a standard sine or cosine function?

• π radians

• 4π radians

• 2π radians

• π/2 radians

Which constants affect the range of sine and cosine functions?

• Period and frequency

• Frequency and phase shift

• Amplitude and phase shift

• Amplitude and vertical shift

What does the amplitude of a sine or cosine function represent?

• The maximum value from the center line

• The period of the function

• The horizontal shift of the function

• The vertical shift of the function

How can the unit circle be used to construct the graph of sine of T?

• By using the diameter of the unit circle

• By using the radius of the unit circle

• By using the y-coordinates of the unit circle

• By using the x-coordinates of the unit circle

What is the typical period of a cosine function without any modifications?

• π/2 radians

• 2π radians

• 4π radians

• π radians

What happens to the graph of a cosine function when the amplitude is increased?

• The period changes

• The peaks and troughs become higher and lower

• The graph shifts vertically

• The graph shifts horizontally

How does a phase shift affect the graph of a sine or cosine function?

• It changes the amplitude

• It changes the period

• It shifts the graph horizontally

• It shifts the graph vertically

What is the midline of a sine or cosine function?

• The maximum value of the function

• The minimum value of the function

• The vertical line that the function oscillates around

• The horizontal line that the function oscillates around

How do you determine the period of a sine or cosine function from its equation?

• By dividing 2π by the coefficient of x

• By looking at the vertical shift

• By looking at the amplitude

• By adding the phase shift to the amplitude