0606/12 May/Jun 2026, Question 1: Trig Graphs: Amplitude and Period
Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 5 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Without a calculator, sketch y = 4 cos x − 2 over −360° to 360°, then state its amplitude, its period, and the k values giving at least two solutions of 4 cos x − 2 = k.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 2 marks
Draw the curve y = 4 cos x − 2 on the given axes for x from −360° to 360°.
- 1Maximum value 4 − 2 = 2 at x = 0°, ±360°
- 2Minimum value −4 − 2 = −6 at x = ±180°
- 3y = −2 (the centre line) at x = ±90°, ±270°
- 4Two full cycles between −360° and 360°
AnswerTwo full cosine cycles: maximum 2 at x = −360°, 0°, 360°; minimum −6 at x = −180° and 180°; passing through (−270, −2), (−90, −2), (90, −2), (270, −2)
Part (b) · 1 mark
State the amplitude of the function 4 cos x − 2.
- 1Amplitude is the coefficient of cos x: 4
Answer4
Part (c) · 1 mark
State the period of the function 4 cos x − 2.
- 1The period of cos x is 360°, unchanged by ×4 or −2
Answer360°
Part (d) · 1 mark
Find all k for which 4 cos x − 2 = k has two or more solutions.
- 1The line y = k must meet the graph at least twice
- 2The graph takes values from −6 to 2, and every value in this range is reached at least twice
- 3−6 ≤ k ≤ 2
Answer−6 ≤ k ≤ 2
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 LemmaraMore past-paper questions on trig graphs: amplitude and period
Also searched as: 0606/12/M/J/26 · 0606_s26_qp_12 · 0606 s26 12 · question 1.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.