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0580/21 May/Jun 2021, 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 = tan x on the given axes from 0° to 360°, then solve 5 tan x = 1 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 tangent curve for x between 0° and 360° on the axes marked at 0, 90°, 180°, 270° and 360°.

  1. 1Draw the curve through (0, 0), (180°, 0) and (360°, 0), rising from left to right.
  2. 2Draw vertical asymptotes at x = 90° and x = 270°: the curve rises towards +∞ just before each and comes up from −∞ just after.
  3. 3This gives three separate branches: 0° to 90°, 90° to 270°, 270° to 360°.

AnswerCorrect sketch

Part (b) · 2 marks

Find all values of x in the range 0° to 360° satisfying 5 tan x = 1.

  1. 1tan x = 1/5 = 0.2
  2. 2x = tan⁻¹(0.2) = 11.30…° ≈ 11.3°
  3. 3tan repeats every 180°: x = 11.30 + 180 = 191.30…° ≈ 191.3°

Answer11.3 or 11.30 to 11.31 and 191.3 or 191.30 to 191.31

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