Grade 12 · CAPS-aligned
Grade 12 Trig Graphs — Period, Amplitude & Transformations
Sketch sin, cos and tan with the correct periods, shifts and restrictions.
Trig graphs sit inside the broader Grade 12 Trigonometry weighting. You're tested on shape, transformations, restrictions and reading values; individual graph-question marks depend on the paper.
Why most learners find this hard
Horizontal shifts (the 'inside-the-bracket' moves) are where most learners get the sign wrong. Slow down on those.
What you'll learn
- Shape of y = sin x, y = cos x, y = tan x on the standard interval
- Amplitude (the 'a' in a·sin x)
- Period (the 'b' in sin(bx))
- Vertical shift (the 'q' in sin x + q)
- Horizontal shift (the 'p' in sin(x − p))
Worked example
Give the amplitude and period of y = 3·cos(2x).
- 1For sine and cosine, amplitude = |a|. Here |3| = 3.
- 2For sine and cosine, period = 360° / |b| when b ≠ 0.
- 3Here b = 2, so period = 360° / |2| = 180°. Tangent graphs use period 180° / |b| and have no amplitude.
Answer: Amplitude 3, period 180° for y = 3·cos(2x).
Exam tips
- Plot 5 key points per cycle, then connect with a smooth curve.
- For horizontal shifts: (x − p) moves the graph to the right by p.
- Always label the y-intercept and any maximum/minimum value clearly.
Get stuck? Use MindMath SA to improve.
Try a 7-day Basic trial or a 7-day Premium trial via the Pricing page.
Start Basic trial