Ratios and Graphs of Trigonometric Functions
Trigonometric graph
The wave-like graph of sine, cosine or tangent over a range of angles.
| English | Trigonometric graph |
|---|---|
| Bahasa Melayu | Graf trigonometri |
| 中文 | 三角函数图 |
How it is used
Sketching y = cos x from 0° to 360° gives a wave starting at (0°, 1), crossing zero at 90° and 270°, reaching −1 at 180° and returning to 1 at 360°. The curve has amplitude 1 and one full cycle in 360°.
Where it shows up in SPM
Trigonometric graphs appear in the Trigonometric Functions chapter of Form 5. In Paper 2 you sketch y = sin x, y = cos x or y = tan x over a stated range, then use the sketch to count how many solutions an equation such as sin x = 0.4 has in that range.
Don't confuse it with
Open the chapter: Ratios and Graphs of Trigonometric Functions →
Frequently asked questions
How do I find the number of solutions from the graph?
Draw a horizontal line at the given value, for example y = 0.4, across your sketch. Each point where this line cuts the curve is one solution.
Counting the crossings inside the stated range gives the number of solutions without solving the equation.
Why does the tangent graph have breaks in it?
Because tan x = sin x / cos x, and at 90° and 270° cos x is zero, so the ratio is undefined. The graph shoots up towards infinity there and starts again on the other side, leaving vertical breaks called asymptotes.
What scale should I use when sketching?
Mark the x-axis in steps of 90° up to the stated range, and the y-axis from −1 to 1 for sine and cosine. Plot the key points at 0°, 90°, 180°, 270° and 360°, then join them with a smooth curve rather than straight segments.