Introduction
This question tests a core trigonometric graph skill that appears very frequently in O-Level A-Maths:
- Identifying amplitude
- Identifying period
- Understanding how coefficients affect graphs
We follow the teacher’s exact board working.
The Question
State the amplitude and period of:
\(y = 4 \cos 2x\)
Step-by-Step Working (Teacher’s Method)
Step 1: Identify the amplitude
The general form of a cosine graph is:
\(y = a \cos(bx)\)
- The amplitude is the absolute value of \(a\).
Here: \(a = 4\)
So, Amplitude = 4
Step 2: Identify the period
For cosine graphs:
\(\text{Period} = \frac{360^\circ}{b} \quad \text{or} \quad \frac{2\pi}{b}\)
In this question: \(b = 2\)
So:
\(\text{Period} = \frac{360^\circ}{2} = 180^\circ\)
\(\text{Period} = \frac{2\pi}{2} = \pi\)
\(\text{Period} = \frac{2\pi}{2} = \pi\)
✅ Final Answer
Amplitude: 4
Period: \(180^\circ\) or \(\pi\)
Period: \(180^\circ\) or \(\pi\)
Key Concepts
| Concept | Why It Matters |
|---|---|
| Amplitude | Determines graph height |
| Coefficient of \(x\) | Controls period |
| Trigonometric graph rules | Common exam-tested knowledge |
| Degree vs radian | Both answers often accepted |
Tips for Students
- Amplitude is always the number in front
- Period depends on the value multiplying \(x\)
- Memorise: \(\tfrac{360^\circ}{b}\) or \(\tfrac{2\pi}{b}\)
- Write units clearly (degrees or radians)
For Parents
Trigonometric graph questions are high scoring when students master:
- Formula recall
- Conceptual understanding
- Exam accuracy
These skills directly impact Paper 1 performance.