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0580/21 Oct/Nov 2023, Question 19: Trigonometric Graphs and Equations

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

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The question, in short

Sketch y = cos x for 0° to 360° on the given axes, then use cos x = 0.21 to find the reflex angle x.

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

Part (a) · 2 marks

Draw the curve y = cos x over 0° ≤ x ≤ 360°, showing key features on the axes marked −1, 0 and 1.

  1. 1Start at (0, 1), go down through (90, 0) to the minimum (180, −1)
  2. 2Rise through (270, 0) back to (360, 1), with a smooth wave shape

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

Part (b) · 2 marks

Given cos x = 0.21, work out the reflex angle x.

  1. 1cos⁻¹(0.21) = 77.87…°
  2. 2Reflex angle x = 360 − 77.87… = 282.12… ≈ 282.1

Answer282.1 or 282.12…

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