Mathematics Advanced Year 11 - Module 2 - Lesson 14
Modelling with Trigonometric Functions
1. Key Ideas
Tides rise and fall. Temperatures peak in summer and dip in winter. Sound waves travel through air. All of these phenomena can be modelled by sinusoidal functions. In this lesson, you will learn how to extract real-world data, build trigonometric models, and use them to make predictions.
- How to calculate amplitude and midline from maximum and minimum values
- Why periodic phenomena are naturally modelled by trig functions
2. Success Criteria
By the end, you should be able to:
- How to calculate amplitude and midline from maximum and minimum values
- How to determine the period from real-world cycles
- How to write a trigonometric model from given data
3. Key Terms
4. Activity: Build the Lesson Map
Use the lesson to complete the table. Keep answers brief but specific.
| Prompt | Your answer |
|---|---|
| Main concept | |
| Important example | |
| Common mistake to avoid | |
| How this links to the next lesson |
5. Short Answer Questions
1. Explain this lesson goal in your own words: "How to calculate amplitude and midline from maximum and minimum values". Use one specific example from the lesson.
2. Apply this idea to a new example: "How to determine the period from real-world cycles". Show your reasoning clearly.
3. Analyse why this idea matters for understanding Modelling with Trigonometric Functions: "How to write a trigonometric model from given data".
6. Extend: Apply the Idea
A student gives a memorised answer about Modelling with Trigonometric Functions but does not use evidence or reasoning.
Improve the answer by writing a stronger response that uses accurate terminology, a relevant example and a clear explanation.
7. Multiple Choice
1. What is the best first step when answering a question about Modelling with Trigonometric Functions?
A. Identify the key concept being tested
B. Write every fact from memory
C. Ignore the command word
D. Skip examples and evidence
2. Which answer would show stronger understanding of Modelling with Trigonometric Functions?
A. An answer with accurate terms and reasoning
B. A copied definition only
C. A single-word response
D. An answer with no example
3. What should you do if a question asks you to explain?
A. Link the idea to a reason or cause
B. List unrelated facts
C. Only draw a diagram
D. Write the shortest possible answer
8. Success Criteria Proof
Finish with evidence that you can do each success criterion.