Lemmara logoLemmaraWorked solution

4MA1/1HR Jan 2023, Question 20: Trigonometric Graphs and Equations

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 2 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

From a sketch of y = a cos(x + b)° on 0 ≤ x ≤ 360, with 0 < b < 180, use the graph's key features to find the constants a and b.

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

Solution · 2 marks

  1. 1The curve rises to 2 and falls to −2, so the amplitude is 2
  2. 2For y = a cos(x + b) the amplitude is a, so a = 2
  3. 3cos of an angle is 1 when that angle is 0 or 360
  4. 4Since 0 < b < 180, the angle x + b runs from b to 360 + b, so within the sketch the maximum is where x + b = 360
  5. 5The sketch is at its maximum at x = 225, so 225 + b = 360
  6. 6b = 360 − 225 = 135

Answera = 2, b = 135

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

Practise more trigonometric graphs and equations questions

Real 4MA1 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: 4MA1 1HR January 2023 · 4MA1/1HR · 4ma1 jan23 1hr · question 20.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.