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MHF4U – 2-3J: Trigami: Unfolding Transformations

Total Marks 28

KICA

K I C A

6 14 4 4

Weight 5%

Learning Goals:

Students will be able to...

 Investigate sine and cosine graphs.

 Investigate reciprocal trigonometric functions.

 Learn how to transform the sine and cosine functions and understand the roles of the

parameters.

 Understand the properties of trigonometric functions.

 Explore how to sketch the graph of a transformed function and determine the properties of a

sinusoidal function from its equation.

 Demonstrate communication skills.

Success Criteria:

I can...

 Graph sinusoidal functions

 Identify transformations of the sine and cosine functions

 State parameters of a transformed function.

 Determine the properties of the trigonometric functions (period, amplitude, axis of curve and

phase shift).

 Use transformed trigonometric functions to model real-world situations.

 Use the mapping rule to transform sinusoidal functions involving the 5 original key points.

 Create expressions for sinusoidal functions given data from a table.

 Provide all reasoning, thinking and logic to justify responses where necessary.

 Use correct notation as learned in LMS.

General Scoring Notes

 All responses and answers must be supported by detailed work and thought process.

 Provide all reasoning, thinking and logic to justify responses where necessary.

 Proper notation from LMS must be present in this evaluation.

 All graphs/sketches done by hand, must have appropriate end behaviors/arrows to correspond to

domain/range and intervals. All sketches must be clear, organized, and well labeled with an

appropriate scale.

 All transformed functions must be in the form 푓(푥)=푎푓(푘(푥−푑))+푐

 Mapping notation must be mapped based on the parameters, a, k, d and c.

 For trigonometric function mapping, you must use the 5 key points defined in LMS

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Overall Communication Marks

This assignment will be graded for your mathematical notation.

Mathematical Notation Communication: 1 Mark

- Function notations are correctly used.

- Proper mathematical form as seen in Rosedale LMS.

(To earn this mark, function notation must be used correctly in every question. No partial marks will be

awarded)

Question 1

In one area of the Bay of Rosedale in a newly discovered earth like planet, the depth of the bay is 22m at

high tide and 2m at low tide. One tidal cycle is completed every 16 hours. Assume that changes in the

depth of the water over time can be modeled by a trigonometric function and also assume low tide

happens at midnight.

a) By applying the definition of a periodic function, explain how this scenario is periodic.

(Application: 2 mark)

b) Create a trigonometric function to model the tide in the Bay of Rosedale. (Inquiry: 5 marks)

c) Determine the mapping rule for your proposed trigonometric function. (Knowledge: 2 mark)

(

푥,푦

)

→

(

______________ ,_____________

)

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d) Identify the parent function for your proposed trigonometric function. Create a table of values for

the parent function and a table of values for your proposed function using your mapping rule.

Please include the mapping on x and y in the first row of the second table. (Knowledge: 4 marks)

Parent Function: ______ Transformed Function Using Mapping: ______________

e) Sketch a graph of your proposed trigonometric function using your table of values. Include proper

scale, axes, and points. (Communication: 3 marks)

f) Calculate the depth of the water at 180 minutes after low tide. (Inquiry: 2 marks)

x y

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g) If the water is at average sea level at 2:00 am, and the tide is coming in, create an equation that

shows how the depth changes over the next 24h. Show your work. You may use a sketch to

support your thinking, no marks will be awarded for a sketch. (Note: The assumption that low tide

happens at midnight, is not applicable in this case.) (Thinking: 3 marks)

h) Model your function with a different trigonometric function. Provide the new function and

explain why the function can be modeled in different ways. (Thinking: 2 marks)

i) Many other phenomena in the real world can be represented with a similar function to the one

used for the tide in Rosedale Bay. Identify 1 real-world scenario or phenomenon (not tides) that

could be modeled using a similar function and explain why this is an appropriate model.

(Application: 2 mark)

j) Not all scenarios that appear periodic are true periodic functions. Identify one scenario that

appears periodic but is actually not a true periodic function. Explain why it is not periodic.

(Inquiry: 2 marks)

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