Lemmara logoLemmaraWorked solution

0580/42 Oct/Nov 2022, Question 9: Trigonometric Graphs and Equations

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 5 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Sketch y = sin x on the given axes for 0° to 360°, then solve 5 sin x + 4 = 0 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 sine curve y = sin x on the axes from 0° to 360°.

  1. 1Start at (0, 0), rise to a maximum at (90, 1)
  2. 2Back through (180, 0), down to a minimum at (270, −1), back up to (360, 0)
  3. 3Draw a smooth wave through these points

AnswerCorrect sketch to go through (0, 0) and (360, 0)

Part (b) · 3 marks

Find the values of x between 0° and 360° satisfying 5 sin x + 4 = 0.

  1. 15 sin x = −4, sin x = −0.8
  2. 2sin⁻¹(0.8) = 53.13…°
  3. 3x = 180 + 53.13 = 233.13… ≈ 233.1°
  4. 4x = 360 − 53.13 = 306.86… ≈ 306.9°

Answer233.1 or 233.13… and 306.9 or 306.86 to 306.87

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: 0580/42/O/N/22 · 0580_w22_qp_42 · 0580 w22 42 · question 9.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.