Additional Mathematics – Trigonometry | e-Consult

Answer 2

• Amplitude \(=|{-2}| = 2\).
• Period \(= \dfrac{2\pi}{|3|}= \frac{2\pi}{3}\).
• There is no vertical shift (the constant term is 0).
• Horizontal shift: write the argument as \(3\left(x+\frac{\pi}{3}\right)\). Hence the graph is shifted \(\frac{\pi}{3}\) units to the left.
• Transformation sequence:

  1. Horizontal stretch/compression by factor \(\frac{1}{3}\) (period becomes \(\frac{2\pi}{3}\)).
  2. Shift left by \(\frac{\pi}{3}\).
  3. Reflect in the x‑axis (multiply by –1).
  4. Vertical stretch by factor 2 (multiply amplitude by 2).