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Cambridge IGCSE Maths (0580) · Topic 6: Trigonometry · 6.4

Cambridge IGCSE Maths 0580 Trigonometric Graphs and Equations Questions

Trigonometric Graphs and Equations questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.

Practise trigonometric graphs and equations →Trigonometric Graphs and Equations notes

What the syllabus asks

Summarised in our own words: check the exact wording in the official 0580 syllabus.

Trigonometric Graphs and Equations questions: Extended

Extended content, for Papers 2 and 4.

Question 1 Extended calculator · easy

Find all the angles \(x\) between \(0°\) and \(360°\) for which \(\sin x = 0.8\). Give your answers correct to 1 decimal place.

Show the worked answer
  1. \(x = \sin^{-1} 0.8 = 53.13\ldots°\).
  2. Sine is also positive in the second quadrant: \(180° - 53.13\ldots° = 126.86\ldots°\).

Answer: \(x = 53.1°\) or \(x = 126.9°\)

Question 2 Extended non-calculator · easy

For the graph of \(y = \cos x\), write down
(a) the greatest value of \(y\)
(b) the least value of \(y\)
(c) the period of the graph, in degrees.

Show the worked answer
  1. The cosine graph goes between \(1\) and \(-1\) and repeats every \(360°\).

Answer: (a) \(1\) (b) \(-1\) (c) \(360°\)

Question 3 Extended calculator · medium

Solve \(\cos x = -0.5\) for \(0° \le x \le 360°\).

Show the worked answer
  1. \(\cos^{-1}(-0.5) = 120°\).
  2. By symmetry of the cosine graph about \(180°\): \(360° - 120° = 240°\).

Answer: \(x = 120°\) or \(x = 240°\)

Question 4 Extended calculator · medium

Solve \(\tan x = 1\) for \(0° \le x \le 360°\).

Show the worked answer
  1. \(\tan^{-1} 1 = 45°\).
  2. The tangent graph repeats every \(180°\): \(45° + 180° = 225°\).

Answer: \(x = 45°\) or \(x = 225°\)

Question 5 Extended calculator · medium

Solve \(\sin x = -0.3\) for \(0° \le x \le 360°\). Give your answers correct to 1 decimal place.

Show the worked answer
  1. \(\sin^{-1} 0.3 = 17.45\ldots°\).
  2. Sine is negative in the third and fourth quadrants: \(180° + 17.45\ldots° = 197.45\ldots°\) and \(360° - 17.45\ldots° = 342.54\ldots°\).

Answer: \(x = 197.5°\) or \(x = 342.5°\)

Question 6 Extended non-calculator · medium

For the graph of \(y = \tan x\), \(0° \le x \le 360°\), write down
(a) the period
(b) the values of \(x\) where the graph crosses the \(x\)-axis
(c) the values of \(x\) where the graph has vertical asymptotes.

Show the worked answer
  1. (a) The tangent graph repeats every \(180°\).
  2. (b) \(\tan x = 0\) where \(\sin x = 0\): \(0°\), \(180°\), \(360°\).
  3. (c) \(\tan x = \frac{\sin x}{\cos x}\) is undefined where \(\cos x = 0\): \(90°\) and \(270°\).

Answer: (a) \(180°\) (b) \(0°, 180°, 360°\) (c) \(90°\) and \(270°\)

Question 7 Extended calculator · hard

Solve \(3\cos x + 1 = 0\) for \(0° \le x \le 360°\). Give your answers correct to 1 decimal place.

Show the worked answer
  1. \(\cos x = -\frac{1}{3}\)
  2. \(x = \cos^{-1}\left(-\frac{1}{3}\right) = 109.47\ldots°\) and \(360° - 109.47\ldots° = 250.52\ldots°\).

Answer: \(x = 109.5°\) or \(x = 250.5°\)

Question 8 Extended calculator · hard

Solve \(2\sin x = \cos x\) for \(0° \le x \le 360°\). Give your answers correct to 1 decimal place.

Show the worked answer
  1. Divide by \(\cos x\): \(2\tan x = 1\), so \(\tan x = 0.5\).
  2. \(x = \tan^{-1} 0.5 = 26.56\ldots°\) and \(26.56\ldots° + 180° = 206.56\ldots°\).

Answer: \(x = 26.6°\) or \(x = 206.6°\)

Examiner Insights: common mistakes in IGCSE Maths 0580, with fixes (our analysis of public sources) →

Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).

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Questions students ask

Which Cambridge 0580 papers can test trigonometric graphs and equations?

Trigonometric Graphs and Equations is Extended content (syllabus 6.4), so it is tested only on the Extended papers, Paper 2 (non-calculator) and Paper 4 (calculator). Core candidates do not need it.

Are these Cambridge past-paper questions?

No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.

Where can I practise more trigonometric graphs and equations questions?

In the 0580 practice for topic 6 (Trigonometry), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.

More trigonometry questions