This common misconceptions covers Common Misconceptions 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 10 of 11 in this topic. Use this common misconceptions to connect the idea to the wider topic before moving on to questions and flashcards.
⚠️ Common Misconceptions
Misconception 1: "The period of y = sin(2x) is 720° (twice 360°)"
When the angle is multiplied by a factor n inside the function, the period DIVIDES by n, it does not multiply. y = sin(2x) completes two full cycles in 360°, so its period is 360° ÷ 2 = 180°. The larger n is, the SHORTER and more compressed the graph becomes. Think of it as squashing the graph horizontally — more cycles fit in the same space. Only y = sin(x/2) would have a longer period of 720°.
Misconception 2: "sin x = 0.5 has only one solution between 0° and 360°"
The sine graph crosses any horizontal line y = k (where −1 < k < 1) TWICE in every 360° period. For sin x = 0.5, the solutions are x = 30° AND x = 150°. The sine graph is symmetric about x = 90°, so the second solution is always 180° − (first solution). For cosine, the graph is symmetric about 0° and 360°, so the second solution is 360° − (first solution). Always check for two solutions in trig equations.
Misconception 3: "y = cos x starts at zero like y = sin x"
y = cos x starts at its MAXIMUM value of 1 when x = 0, not at zero. This is because cos 0° = 1 (the cosine of zero degrees is 1). The cosine graph looks like the sine graph shifted 90° to the left — it starts at a peak rather than at the middle. If you mistakenly sketch cos as starting at zero, all your key points will be wrong. Always mark (0°, 1) as the starting point for the cosine graph.
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.