3.2 Modeling data and scenarios with sinusoidal functions

• What is the general form of a sinusoidal function?

  $y =$$A *$$sin(Bx + C) +$$D$
• The parameter `A` in a sinusoidal function represents the amplitude
• The period of a sinusoidal function is calculated as 2π/|B|.
• Match the parameter of a sinusoidal function with its effect:

  Amplitude ↔️ Determines wave height

  Period ↔️ Controls how often the wave repeats

  Phase Shift ↔️ Shifts the wave horizontally

  Vertical Shift ↔️ Moves the wave up or down
• What are some real-world phenomena that can be modeled using sinusoidal functions?

  Seasonal temperature changes
• The amplitude of a sinusoidal function determines the length of its cycle.

  False
• The period of a sinusoidal function is the length of one complete cycle
• For the sinusoidal function `y = 3sin(2x - π) + 1`, what is the period?

  $\pi$
• The phase shift for `y = 3sin(2x - π) + 1` is π/2.
• Order the parameters of a sinusoidal function by their primary effect on the wave:

  1️⃣ Amplitude

  2️⃣ Period

  3️⃣ Phase Shift

  4️⃣ Vertical Shift
• For the sinusoidal function `y = 2sin(3x - π/2) + 1`, the phase shift is \pi/6
• The period of a sinusoidal function is calculated as 2π/|B|.
• What parameter of a sinusoidal function represents the difference between the average high and low temperatures in a seasonal temperature model?

  Amplitude
• What is the general form of a sinusoidal function?

  $y =$$A *$$sin(Bx + C) +$$D$
• The amplitude of a sinusoidal function controls the height of the wave
• The period of a sinusoidal function is calculated as T = 2π/|B|</latex>.
• How is the phase shift of a sinusoidal function calculated?

  $- C / B$
• When modeling seasonal temperature changes, the amplitude represents the difference between the average high and low temperatures
• Order the parameters used in a sinusoidal function to model average monthly temperature:

  1️⃣ Amplitude (A)

  2️⃣ Period (T)

  3️⃣ Phase Shift (C)

  4️⃣ Vertical Shift (D)
• What is the effect of adjusting the vertical shift (D) in a sinusoidal function?

  Raises or lowers the wave
• Match the sinusoidal parameter with its effect:

  Amplitude (A) ↔️ Controls wave height

  Period (T) ↔️ Controls how often the wave repeats

  Phase Shift (C) ↔️ Controls horizontal shift

  Vertical Shift (D) ↔️ Controls vertical displacement
• The period of a sinusoidal function is calculated using the formula T = 2π/|B|</latex>.
• To model the average monthly temperature, the vertical shift (D) represents the average yearly temperature
• What type of functions are sinusoidal functions?

  Trigonometric
• What does the amplitude (A) measure in a sinusoidal function?

  Height of the wave
• The period of a sinusoidal function is calculated as $T =$$2π / |B|$.
• The phase shift of a sinusoidal function is calculated as -C/B
• What does the amplitude (A) control in a sinusoidal function?

  Maximum and minimum values
• The period (T) of a sinusoidal function determines how often the wave repeats.
• The phase shift (C) in a sinusoidal function moves the wave left or right
• What does the amplitude represent in the context of seasonal temperature changes?

  Difference between high and low temperatures
• The period in sinusoidal modeling of seasonal temperature changes is one year
• What does the phase shift indicate in sinusoidal modeling of seasonal temperature changes?

  When seasons peak
• Amplitude controls the maximum and minimum values of a sinusoidal function.
• What is the formula for the period of a sinusoidal function?

  T = \frac{2\pi}{|B|}</latex>
• The phase shift of a sinusoidal function moves the wave left or right
• What is the amplitude of the sinusoidal function $y =$$2\sin(3x - \frac{\pi}{2}) +$$1$?


  2
• The period of the sinusoidal function y = 2\sin(3x - \frac{\pi}{2}) + 1</latex> is $\frac{2\pi}{3}$
• The period of a sinusoidal function is calculated as $T =$$\frac{2\pi}{|B|}$.
• How is the phase shift calculated in a sinusoidal function?

  $\frac{ - C}{B}$