Task Sets: Model periodic phenomena - Common Core Math - HS Functions

Concepts

Which statement correctly identifies all three parameters of the function
$y = 4\sin(3x) + 7$ ?

Amplitude = 4, period = $3$ , midline $y = 7$

Amplitude = 4, period = $\dfrac{2\pi}{3}$ , midline $y = 7$

Amplitude = 4, period = $6\pi$ , midline $y = 7$

Amplitude = 7, period = $\dfrac{2\pi}{3}$ , midline $y = 4$

A function of the form $y = -5\cos\!\left(\tfrac{\pi}{6}x\right) + 10$
is used to model a periodic phenomenon. What is the amplitude of this
function? Enter a number.

A Ferris wheel seat is at its lowest point at $t = 0$ . Which function
form best describes the height $h(t)$ without requiring a horizontal
phase shift?

$h(t) = A\sin(Bt) + D$

$h(t) = A\cos(Bt) + D$

$h(t) = -A\cos(Bt) + D$

$h(t) = -A\sin(Bt) + D$

Procedures

A buoy rises and falls with the waves. Its highest point is 3.8 meters
above sea level and its lowest point is 0.2 meters above sea level.
What is the amplitude of the sinusoidal model, in meters?

Using the same buoy scenario (max 3.8 m, min 0.2 m, one complete cycle
every 4 seconds), what is the midline of the model, in meters?

For the buoy scenario (period = 4 seconds), what is the value of $B$
in the equation $h(t) = A\sin(Bt) + D$ ? Express your answer as a
decimal rounded to three decimal places. (Use $\pi \approx 3.14159$ .)

A temperature in a desert town varies periodically. The high is 104°F
and the low is 68°F, with a 24-hour period. The temperature is at its
maximum at $t = 0$ hours. Which equation correctly models the
temperature $T(t)$ ?

$T(t) = 18\cos\!\left(\dfrac{\pi}{12}t\right) + 86$

$T(t) = 36\cos\!\left(\dfrac{\pi}{12}t\right) + 86$

$T(t) = 18\cos\!\left(\dfrac{\pi}{12}t\right) + 104$

$T(t) = 18\cos\!\left(24t\right) + 86$

HSF.TF.B.5 Tutor Intake — Sinusoidal Modeling

Concepts

Procedures