This study notes covers Worked Examples within Trig Graphs for GCSE Mathematics. Revise Trig Graphs in Graphs for GCSE Mathematics with 11 exam-style questions and 11 flashcards. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. It is section 9 of 11 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 9 of 11
Practice
11 questions
Recall
11 flashcards
✏️ Worked Examples
Example 1: Identifying Key Points on Trig Graphs
Question: State the maximum and minimum values of y = 3 sin x, and describe how it differs from y = sin x.
Show Solution
Standard y = sin x: maximum = 1 at x = 90°, minimum = -1 at x = 270°
y = 3 sin x: every y-value is multiplied by 3 — amplitude = 3
Maximum = 3 (at x = 90°), minimum = -3 (at x = 270°)
Period: still 360° — only the amplitude changes, not the period
Answer: Maximum = 3 at 90°, minimum = -3 at 270°. Same shape as sin x but vertically stretched by factor 3.
Example 2: Solving a Trigonometric Equation Using the Graph
Question: Find all solutions to sin x = 0.5 for 0° ≤ x ≤ 360°.
Show Solution
Step 1: First solution — x = sin⁻¹(0.5) = 30°
Step 2: Use symmetry of the sine graph — the sine curve is symmetric about x = 90°, so the second solution = 180° - 30° = 150°
Step 3: Check both solutions
sin 30° = 0.5 ✓ sin 150° = sin(180° - 30°) = sin 30° = 0.5 ✓
Answer: x = 30° or x = 150°
Example 3: Describing a Transformation of a Trig Graph
Question: Describe the transformation that maps y = cos x onto y = cos(2x).
Show Solution
Step 1: Identify the change — the x has been replaced by 2x (inside the function)
Step 2: Apply the transformation rule — f(ax) compresses horizontally by factor a. Here a = 2.
Step 3: Calculate new period — Period of cos x = 360°. Period of cos(2x) = 360° ÷ 2 = 180°
Effect: The graph is compressed horizontally — two complete cycles fit in 360° instead of one.
Answer: Horizontal compression by scale factor ½. New period = 180°. Amplitude unchanged (still 1).
Keep building this topic
Read this section alongside the surrounding pages in Trig Graphs. That gives you the full topic sequence instead of a single isolated revision point.
Practice Questions for Trig Graphs
What is the period of the graph y = sin x?
Explain the relationship between the graphs of y = sin x and y = cos x.
Quick Recall Flashcards
11 questions on Trig Graphs — practise free
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