Alg2 Lesson 4T.7: A Model for Periodic Phenomena

Lesson 4T.7: A Model for

Periodic Phenomena

Obj: I can identify key characteristics of a sinusoidal
function. I can construct a sinusoidal function to
model a cyclical relation that has a specified
frequency, period, amplitude, and phase shift.

EQ: How to i formulate sinusoidal models?

Roles:
Facilitator
Scribe
Resourcer
Includer

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas and prior info
● Help explain ideas to each other
● Own your ideas and work
● Record ideas in your journal
● Answer Questions on Slides
● Follow your team roles

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Scribe

• Make sure peers organize their results on their own papers.

• Remind peers to use color, arrows, and other math tools to
communicate your mathematics, reasons, and connections.

• Be ready to join the teacher for a huddle.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties that may arise.

Includer

• Make sure that all peers are talking about their work.

• Helps keep peers’ voice volume low.

• Encourages everyone to ask questions.

• Communicates conflicts or questions to the teacher.

● Check off tasks & skills on calendar.

● Select skills to work on.

● Work on Deltamath.

Remember to work on the following too…

Multiple Choice

Which of the following types of functions best describes sunrise and sunset?

• Periodic function
• Logarithmic function
• Exponential function
• Power function

Part 1: Analyzing a Circular

Motion Context

Let f(x) = |x|.

Function Type:

Identify each transformation:

f(x) + 2:

f(x + 2):

2f(x):

-f(x):

Match

Match each transformation from f(x) = |x|

• f(x) + 2

• f(x + 2)

• 2f(x)

• f(2x)

• -f(x)

up

left

Vertical Stretch

Horizontal Compression

Reflection across x-axis

• up

• left

• Vertical Stretch

• Horizontal Compression

• Reflection across x-axis

Dropdown

The maximum and minimum heights represent the ​

Select answer

of the function.

Suppose that Mira completes two revolutions on the Ferris wheel. What would be
the contextual domain of the function? The contextual domain is 0 <= t <= ​

Select answer

,
where t is the number of minutes since she boarded the Ferris wheel.

Part 2: Transforming a

Sinusoidal Function

We know that a sine function would be an appropriate model for this scenario. How could we make modifications to the sine parent function so that it matches a Ferris wheel context? What transformations should we use to construct an algebraic representation of
the function model?

y = asin(b(x - c)) + d

Midline: the horizontal line over which the graph of the
sinusoidal function oscillates. (d)

Amplitude: describes the vertical scaling of the graph. (a)

Period: the length of the interval of the input values over
which the function completes one full cycle. (2pi/b)

Phase Shift: describes the horizontal translation of the
graph. (c)

​(Write these in journal!)

Part 3: Interpreting a Model

for Periodic Phenomena

Random Question of the Day Time

https://wheelofnames.com/4ke-epz We’ll spin
the wheel as a class and spend a minute or so
discussing our answers.