Sinusoidal Applications

In the functions f(x)=Asin[B(x + C)] + D,

D represents what?

(More than one answer may be possible)

• Amplitude

• Horizontal Translation

• Phase Shift

• Vertical Shift

This equation models the data from question 1, where x stands for month of the year and y stands for daylight hours.  Use the equation to predict th length of daylight during the month of May.

• 5 hours
• 14.28 hours
• 11.9 hours
• 13.85 hours

What is the period of y = 2cos(4x)-5

• π/3

• 6π

• 2π/3

• π/2

At a pier, scientists measure the depth of the water according to the tides.  At high tide, the water depth is 8 feet.  At low tide, 6.2 hours later, the depth is 5 feet.  What is the average depth of the water?

• 6.5 feet

• 1.5 feet

• 1.57 feet

• 6.8 feet

Which equation represents the graph?

• y = cos x – 3
• y = sin x – 3
• y = cos (x – 3)
• y = sin (x – 3)

At a pier, scientists measure the depth of the water according to the tides.  At high tide, the water depth is 8 feet.  At low tide, 6.2 hours later, the depth is 5 feet.  Calculate the sinusoidal regression equation that models this scenario.

• 1.5sin(0.507x + 1.57) + 6.5
• 0.507 sin(1.5x + 6.5) + 1.57
• y = 6.8x
• y = 6.2x + 5

Find the equation of the midline of the graph shown.

• y = 1
• y = 2
• y = 3
• y = 0

What is the amplitude of the graph?

• 3

• 2

• -3

• -2

What is the equation of graph? 

• y = sin 5x
• y =  cos 5x
• y = 5 sin x
• y = 5 cos x