Key Features of Sinusoidal Functions

What is the amplitude of the graph?

• 3

• 2

• -3

• -2

Consider a Ferris wheel, moving in constant motion. At its lowest height of 2 metre above the ground, it loads passengers. It carries passengers to a height of at most 14 metres. How high is the middle of Ferris wheel off the ground?

• 2m

• 8m

• 14m

• 12m

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

• π/3

• 6π

• 2π/3

• π/2

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

D represents what?

(More than one answer may be possible)

• Amplitude

• Axis of the Curve

• Phase Shift

• Vertical Shift

• Horizontal Translation

How do we find the period of the sinusoidal function below?
f(x) = asin(kx)+d

A section of a rollercoaster is in the shape of a sinusoidal curve shown below. It has a maximum height above the ground of 51 m and a minimum of 1 m. The equation can be written in the form h = Asin(Bd) + C:

What is the value of A?

• -20m

• 50m

• 25m

• 15m

• 8

The temperature in an office is controlled by an electronic thermostat. The temperatures vary according to the sinusoidal function:

y = 5 sin( π/12 (x – 11)) +18

where y is the temperature (ºC) and x is the time in hours past midnight. What are the minimum and maximum temperatures in the office?

• 12ºC and 23ºC

• 13ºC and 23ºC

• 5ºC and 18ºC

• 11ºC and 23ºC

What is the equation of graph? 

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