Mathematics Advanced Year 11 - Module 2 - Lesson 12
Phase Shifts and Horizontal Translations
1. Key Ideas
A wave that starts at its peak is different from a wave that starts at zero — even if they have the same amplitude and period. This difference is called a phase shift . In this lesson, you will learn how horizontal translations affect trigonometric graphs, how to identify phase shifts from equations, and how phase shifts appear in real-world phenomena like sound, light, and tides.
- The general form of transformed sine and cosine functions
- Why $y = \sin(x - c)$ shifts right by $c$ units
2. Success Criteria
By the end, you should be able to:
- The general form of transformed sine and cosine functions
- How to identify amplitude, period, phase shift, and vertical shift
- The relationship between phase shift and horizontal translation
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: "The general form of transformed sine and cosine functions". Use one specific example from the lesson.
2. Apply this idea to a new example: "How to identify amplitude, period, phase shift, and vertical shift". Show your reasoning clearly.
3. Analyse why this idea matters for understanding Phase Shifts and Horizontal Translations: "The relationship between phase shift and horizontal translation".
6. Extend: Apply the Idea
A student gives a memorised answer about Phase Shifts and Horizontal Translations 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 Phase Shifts and Horizontal Translations?
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 Phase Shifts and Horizontal Translations?
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.