Lemmara logoLemmaraWorked solution

0580/21 Oct/Nov 2022, Question 22: Trigonometric Graphs and Equations

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 4 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Sketch y = cos x between 0° and 360° on axes marked −1, 0, 1 and 360°, then solve cos x = −1/2 over the same interval.

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

Part (a) · 2 marks

Draw the cosine curve from 0° to 360° on the given axes, showing correct values at key points.

  1. 1Start at (0, 1)
  2. 2Cross the x-axis at 90° and 270°
  3. 3Minimum at (180, −1), back up to (360, 1) with a smooth curve

AnswerCorrect sketch through (0, 1), (360, 1) and (180, −1)

Part (b) · 2 marks

Find all angles x between 0° and 360° satisfying cos x = −1/2.

  1. 1cos⁻¹(−1/2) = 120°
  2. 2By symmetry of the cosine graph, 360 − 120 = 240°
  3. 3x = 120 or x = 240

Answer120, 240

Stuck on a step? Read the free lesson: Trigonometric Graphs and Equations

Practise more trigonometric graphs and equations questions

Real 0580 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 trigonometric graphs and equations

Also searched as: 0580/21/O/N/22 · 0580_w22_qp_21 · 0580 w22 21 · question 22.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.