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.
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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°.
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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).
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Step 1: Identify the change — the x has been replaced by 2x (inside the function)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).
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.
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.