A-level · Trigonometry

Solving trigonometric equationsExam-style questions

The full method for solving trig equations in a range — quadratics in sin/cos, using sin²+cos²≡1 to convert a mixed equation, and transformed arguments like sin 2x and cos(x − 30°) where the interval must change.

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13 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    Solve sin⁡2x∘=0.5\sin 2x^\circ = 0.5 for 0≤x≤3600 \le x \le 360.
    Level 3 · 4 marksTry it
  2. 2
    Solve cos⁡(x−30)∘=0.5\cos(x - 30)^\circ = 0.5 for 0≤x≤3600 \le x \le 360.
    Level 3 · 3 marksTry it
  3. 3
    Solve 4sin⁡2x∘=34\sin^2 x^\circ = 3 for 0≤x≤3600 \le x \le 360.
    Level 3 · 3 marksTry it
  4. 4
    Solve the equation 3sin⁡2θ+4cos⁡θ=43\sin^{2}\theta + 4\cos\theta = 4 for 0∘⩽θ⩽360∘0^{\circ} \leqslant \theta \leqslant 360^{\circ}. (5 marks)
    Level 3 · 5 marksTry it
  5. 5
    Solve the equation

    4sin⁡2θ=3+cos⁡θ4\sin^2\theta = 3 + \cos\theta

    for 0∘≤θ<360∘0^\circ \le \theta < 360^\circ, giving your answers to 1 decimal place. (6 marks)
    Level 3 · 6 marksTry it

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