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WMA11/01 Jun 2025, Question 4: Trig Graphs: Amplitude and Period

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 6 marks

The question, in short

Use the graph of y = 4 cos x in degrees to identify key points and count how many times given equations hold over large degree intervals.

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

Part (a) · 1 mark

Find the coordinates of the point where the curve first crosses the positive x-axis going up.

  1. 1cos x = 0 at x = 90°, 270°, …
  2. 2P is the second positive x-intercept, where the curve rises: P = (270, 0)

Answer(270, 0)

Part (b) · 2 marks

Find the coordinates of the first minimum point lying to the left of the y-axis.

  1. 1The minimum value of 4 cos x is −4, at x = ±180°, …
  2. 2Q is the minimum just left of the y-axis: Q = (−180, −4)

Answer(−180, −4)

Part (ci) · 1 mark

Count how many times 4 cos x equals 3 for 0 < x ≤ 18000°.

  1. 1cos x = 3/4 has 2 solutions in each 360° cycle
  2. 20 < x ≤ 18000° is 18000/360 = 50 cycles
  3. 3Number of solutions = 50 × 2 = 100

Answer100

Part (cii) · 1 mark

Count how many times 5 + 4 cos x equals 1 for −720° < x ≤ 720°.

  1. 15 + 4 cos x = 1 gives cos x = −1
  2. 2x = −540°, −180°, 180°, 540° in −720° < x ≤ 720°
  3. 3Number of solutions = 4

Answer4

Part (ciii) · 1 mark

Count how many times 4 cos x − 3 equals 1 for −1080° ≤ x ≤ 1080°.

  1. 14 cos x − 3 = 1 gives cos x = 1
  2. 2x = −1080°, −720°, −360°, 0°, 360°, 720°, 1080° (both ends included)
  3. 3Number of solutions = 7

Answer7

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