Graphs of Sine and Cosine

What is the distance between the max and min values in the equation 

y = 4 sin (x) + 2 ?

• 4

• 6

• 8

• 2 $\pi$

What is the period of the equation y = 3 cos (6x) ?

• 3

• $\pi$ /3

• $\pi$ /6

• 6 $\pi$

What is the midline of the equation y = 4 sin (2x) - 3

• y = -3

• y = 2

• y = 4

• y = 2 $\pi$

Which equation below has a period of  $\pi$  /4 ?

• y = 4 sin (1/4x) 

• y = -3 cos (8x) + 1

• y = 1/4 cos (2x)

• y = sin (4x)

The graph of a sine function has a midline at y = 4, a maximum value at 7, and a period of 2 $\pi$  /3.  

• y = 4 sin (2/3x) + 7

• y = 3 sin (2/3x) + 4

• y = 3 sin (3x) + 4

• y = 6 sin (3x) + 4

A cosine function has a max value at 8, a min value at 4, and a period of 2 $\pi$  . Which equation below matches this description?

• y = 4 cos (x) + 6

• y = 4 cos (x) + 8

• y = 2 cos (x) + 4

• y = 2 cos (x) + 6

What is the equation for the given graph?

• y = 5 sin (1/3x) + 3

• y = 2 sin (3x) + 3

• y = 2 sin (3x) + 5

• y = 3 sin (1/3x) + 5

• y = 3 cos (x) - 2

• y = 6 cos (x) - 3

• y = 3 cos (2x) - 2

• y = 6 cos (2x) - 3

What does the period tell you about a sine or cosine graph?

• The distance from the midline to the max value

• Half the distance between the max and min values

• How often does the pattern of the graph repeat between 0 and 2 $\pi$

• The frequency with which the pattern of a graph repeats along the x-axis

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

•  $\pi$  /3

• 6 $\pi$  

• 3 $\pi$  

•  $\pi$  /6