Additional Mathematics – Trigonometry | e-Consult
Trigonometry (1 questions)
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Answer 2
- Amplitude = 3
- Period = \(\displaystyle\frac{2\pi}{0.5}=4\pi\)
- Phase shift = 0 (no horizontal translation)
- Vertical shift = +2
The cosine factor is multiplied by –3, so the graph is reflected vertically.
| Maximum y = 5 occurs when cos(0.5x)=–1 → 0.5x = π + 2πn → x = 2π + 4πn |
Within –π ≤ x ≤ 3π the admissible n are 0 and –1, giving x = 2π and x = –2π (the latter is outside the interval). Hence the only x‑value in the domain is x = 2π. The graph shows a peak at (2π, 5) and repeats every 4π.