Ratios and Graphs of Trigonometric Functions · 6.2.1
Graphs of sin x, cos x and tan x
Students plot the three basic trigonometric graphs over one full cycle from 0° to 360° using a table of values, then examine features such as maximum and minimum values, x-intercepts, shape, and (for tangent) the undefined points, comparing how sine, cosine and tangent differ in appearance and behaviour.
The official learning standard (6.2.1)
“Draw graphs of trigonometric functions y = sin x, y = cos x and y = tan x for 0° ≤ x ≤ 360°, hence compare and contrast the characteristics of the graphs.”
What it means
Students plot the three basic trigonometric graphs over one full cycle from 0° to 360° using a table of values, then examine features such as maximum and minimum values, x-intercepts, shape, and (for tangent) the undefined points, comparing how sine, cosine and tangent differ in appearance and behaviour.
How it is examined
In Paper 2, students are typically given a table of values to complete and asked to plot the graph on graph paper, sometimes using the graph to read off solutions. Paper 1 may test recognition of a graph's shape or characteristics (such as its maximum value or period) as an objective item.
Worked example
For the graph of y = sin x, 0° ≤ x ≤ 360°, state (a) the amplitude, (b) the period, and (c) the x-intercepts.
- The graph of y = sin x reaches a maximum of 1 and a minimum of -1, so the amplitude = 1.
- One complete wave is formed from x = 0° to x = 360°, so the period = 360°.
- sin x = 0 at x = 0°, 180° and 360°, so these are the x-intercepts.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Why does the tangent graph look so different from sine and cosine?
Sine and cosine are smooth, continuous waves bounded between -1 and 1, while tangent is unbounded and repeats every 180° instead of 360°. Tangent also has vertical asymptotes at 90° and 270°, where the graph shoots up or down without ever touching those x-values.
How do I choose x-values for my table when plotting these graphs?
Use evenly spaced angles across the full range, typically every 30° or 45° from 0° to 360°, so the shape of the curve is captured smoothly. For y = tan x, avoid listing x = 90° and 270° directly since the function is undefined there.
What does 'amplitude' actually mean for these graphs?
Amplitude measures how far the graph rises above (or falls below) its middle line, it equals half the difference between the maximum and minimum values. For the basic graphs y = sin x and y = cos x, this works out to 1, since they range from -1 to 1.
Tangent graphs do not have an amplitude since they are unbounded.