Lemmara logoLemmaraWorked solution

0580/22 Feb/Mar 2024, Question 23: Trigonometric Graphs and Equations

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 4 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Sketch y = cos x on the given axes for 0° to 360°, then solve cos x = 0.294 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 on the axes from 0° to 360°, marking key features such as the maximum, minimum and intercepts.

  1. 1Start at (0, 1), fall through (90, 0) to the minimum (180, −1)
  2. 2Rise through (270, 0) back to (360, 1), as a smooth wave

AnswerCorrect sketch to go through (0, 1), close to (360, 1) and reasonably close to (180, −1)

Part (b) · 2 marks

Find all values of x between 0° and 360° satisfying cos x = 0.294.

  1. 1x = cos⁻¹(0.294) = 72.9°
  2. 2By symmetry of the cosine curve, x = 360 − 72.9 = 287.1°
  3. 3x = 72.9° and 287.1°

Answer72.9 and 287.1

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: 0580/22/F/M/24 · 0580_m24_qp_22 · 0580 m24 22 · question 23.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.