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0606/23 May/Jun 2025, Question 5: Trig Graphs: Amplitude and Period

Cambridge IGCSE Additional Mathematics 0606 · Paper 23 (Calculator) · Calculator · 4 marks

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The question, in short

Radians throughout. For the function 5 tan(x/4) + 1, state its period, then sketch it on the given axes from −2π to 4π, giving the y-intercept and asymptote positions.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 1 mark

State the period of 5 tan(x/4) + 1, with angles in radians.

  1. 1Period of tan(x/4) = π ÷ (1/4) = 4π

Answer4π

Part (b) · 3 marks

Sketch y = 5 tan(x/4) + 1 for −2π ≤ x ≤ 4π, state the y-axis intercept and show where the asymptotes lie.

  1. 1Asymptotes where x/4 = ±π/2, i.e. x = −2π and x = 2π
  2. 2When x = 0, y = 5 tan 0 + 1 = 1
  3. 3When x = 4π, y = 5 tan π + 1 = 1
  4. 4Increasing branch between −2π and 2π, and a second increasing branch from 2π to 4π

AnswerTwo tan branches: one increasing from x = −2π to x = 2π through (0, 1), and one increasing from x = 2π to x = 4π reaching y = 1 at x = 4π; vertical asymptotes at x = −2π and x = 2π; y-intercept 1

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