Lemmara logoLemmaraWorked solution

0606/22 Feb/Mar 2026, Question 6: Trig Graphs: Amplitude and Period

Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 5 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

For y = 1 + tan(1/2 x) with x in degrees, use the given graph to find its period and the equation of asymptote A, then sketch y = 3 cos 2x + 1 for −180° ≤ x ≤ 180°.

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

Part (ai) · 1 mark

State the period of 1 + tan(1/2 x), with x measured in degrees.

  1. 1The period of tan x is 180°
  2. 2tan((1/2)x) has period 180° ÷ (1/2) = 360°

Answer360°

Part (aii) · 1 mark

Give the equation of asymptote A shown on the graph.

  1. 1Asymptotes of tan((1/2)x) where (1/2)x = 90° + 180°n, i.e. x = ±180°, ±540°, …
  2. 2Asymptote A is the second one to the right of the y-axis: x = 540

Answerx = 540

Part (b) · 3 marks

Sketch y = 3 cos 2x + 1 on the axes for −180° ≤ x ≤ 180°, showing key features.

  1. 1Period = 360° ÷ 2 = 180°, so two cycles between −180° and 180°
  2. 2Amplitude 3, midline y = 1
  3. 3Maximum 3 + 1 = 4 at x = −180°, 0°, 180°
  4. 4Minimum −3 + 1 = −2 at x = −90°, 90°

AnswerCosine curve with two full cycles in −180° ≤ x ≤ 180°, midline y = 1, maximum 4 (at x = −180°, 0°, 180°) and minimum −2 (at x = −90°, 90°)

Stuck on a step? Read the free lesson: Trig Graphs: Amplitude and Period

Practise more trig graphs: amplitude and period questions

Real 0606 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on trig graphs: amplitude and period

Also searched as: 0606/22/F/M/26 · 0606_m26_qp_22 · 0606 m26 22 · question 6.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.