Mathematics Advanced Year 11 - Module 2 - Lesson 10
Graphs of Sine and Cosine
1. Key Ideas
The graphs of $y = \sin x$ and $y = \cos x$ are among the most important in mathematics. They model everything from sound waves to planetary orbits. In this lesson, you will learn the key features of these graphs — amplitude, period, and intercepts — and discover how to transform them into more general sinusoidal functions.
- The shape and key features of $y = \sin x$ and $y = \cos x$
- Why sine and cosine are periodic with period $2\pi$
2. Success Criteria
By the end, you should be able to:
- The shape and key features of $y = \sin x$ and $y = \cos x$
- How to find amplitude, period, and vertical shift
- The relationship between degrees and radians in graphing
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 shape and key features of $y = \sin x$ and $y = \cos x$". Use one specific example from the lesson.
2. Apply this idea to a new example: "How to find amplitude, period, and vertical shift". Show your reasoning clearly.
3. Analyse why this idea matters for understanding Graphs of Sine and Cosine: "The relationship between degrees and radians in graphing".
6. Extend: Apply the Idea
A student gives a memorised answer about Graphs of Sine and Cosine 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 Graphs of Sine and Cosine?
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 Graphs of Sine and Cosine?
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.