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4PM1/01 Jun 2019, Question 7: The Addition Formulae

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 12 marks

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The question, in short

Solve a trigonometric product equation in degrees, prove a tangent identity from a sine equation, then use it to solve a related equation in y.

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

Part (a) · 2 marks

Solve (3 cos θ + 5)(5 sin θ − 3) = 0 for 0 ≤ θ < 180°, giving angles to one decimal place.

  1. 1cos θ = −5/3 is not possible
  2. 2sin θ = 3/5
  3. 3θ = 36.9° or 180° − 36.9° = 143.1°

Answerθ = 36.9°, 143.1°

Part (b) · 5 marks

Show that 8 sin(x − α) = 3 sin(x + α) rearranges to 5 tan x = 11 tan α.

  1. 18(sin x cos α − cos x sin α) = 3(sin x cos α + cos x sin α)
  2. 25 sin x cos α = 11 cos x sin α
  3. 3Divide by cos x cos α: 5(sin x/cos x) = 11(sin α/cos α)
  4. 45 tan x = 11 tan α

Answer5 tan x = 11 tan α shown

Part (c) · 5 marks

Hence solve 8 sin(2y − 30°) = 3 sin(2y + 30°) for 0 ≤ y < 180°, to one decimal place.

  1. 1x = 2y, α = 30°: 5 tan 2y = 11 tan 30°
  2. 2tan 2y = (11/5) tan 30° = 1.270…
  3. 32y = 51.78…° or 231.78…°
  4. 4y = 25.9° or 115.9°

Answery = 25.9°, 115.9°

Stuck on a step? Read the free lesson: The Addition Formulae

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