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0606/21 May/Jun 2026, Question 2: Solving Trig Equations

Cambridge IGCSE Additional Mathematics 0606 · Paper 21 (Calculator) · Calculator · 7 marks

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The question, in short

For the function 4 cos(x/8) + 2, find its amplitude and period in degrees, solve the equation equal to zero over −1080° ≤ x ≤ 1080°, and sketch its graph on the given axes.

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

Part (a) · 1 mark

State the amplitude of 4 cos(x/8) + 2.

  1. 1Amplitude is the coefficient of cos: 4

Answer4

Part (b) · 1 mark

State the period of 4 cos(x/8) + 2, giving the answer in degrees.

  1. 1Period = 360° ÷ (1/8)
  2. 2= 2880°

Answer2880

Part (c) · 3 marks

Find all solutions of 4 cos(x/8) + 2 = 0 in the interval −1080° ≤ x ≤ 1080°.

  1. 1cos(x/8) = −1/2
  2. 2x/8 = 120° or x/8 = −120°
  3. 3x = 960° or x = −960°

Answerx = ±960°

Part (d) · 2 marks

Draw the curve y = 4 cos(x/8) + 2 on the axes for −1080° ≤ x ≤ 1080°.

  1. 1Maximum value 4 + 2 = 6 at x = 0
  2. 2Half a period is 1440°, so only one turning point in the domain
  3. 3y = 0 at x = ±960°
  4. 4At x = ±1080°: y = 4 cos 135° + 2 ≈ −0.83

AnswerSmooth cosine-shaped curve with a single maximum at (0, 6), crossing the x-axis between 900° and 1080° and between −900° and −1080°, ends at about (±1080°, between 0 and −2)

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