Grade 12 · CAPS-aligned
Grade 12 Trig Graphs — Period, Amplitude & Transformations
Sketch sin, cos, tan with shifts in your sleep. Worth 15+ marks.
Trig graphs in Grade 12 are a guaranteed 15-mark question. You're tested on shape, transformations, and reading values. If your Grade 11 trig is solid, this is one of the safest mark-gathering topics in Paper 2.
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).
- 1Amplitude is the coefficient in front: |3| = 3
- 2Period of cos x is 360°. With cos(bx), period = 360° / b.
- 3Here b = 2, so period = 360° / 2 = 180°
Answer: Amplitude 3, period 180°.
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? Ask the AI coach.
Free account. 5 coach questions a day. CAPS-aligned, in plain English.
Start free