A-level · Trigonometry

Double-angle formulaeExam-style questions

The double-angle formulae for sin 2A, cos 2A (three forms) and tan 2A, where they come from, choosing the right form of cos 2A, and using them to solve equations and find exact values.

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

DifficultyAllLevel 3Level 4Level 5
  1. 1
    Given that sin⁡θ=35\sin\theta = \frac{3}{5} and θ\theta is acute, find the exact values of (a) sin⁡2θ\sin 2\theta,
    (b) cos⁡2θ\cos 2\theta,
    (c) tan⁡2θ\tan 2\theta.
    Level 3 · 4 marksTry it
  2. 2
    Prove that sin⁡2θ1+cos⁡2θ≡tan⁡θ\dfrac{\sin 2\theta}{1 + \cos 2\theta} \equiv \tan\theta.
    Level 3 · 2 marksTry it
  3. 3
    Solve sin⁡2x=sin⁡x\sin 2x = \sin x for 0≤x≤2π0 \le x \le 2\pi, giving your answers as exact multiples of π\pi.
    Level 3 · 3 marksTry it
  4. 4
    Solve cos⁡2x=cos⁡x\cos 2x = \cos x for 0≤x≤2π0 \le x \le 2\pi, giving your answers as exact multiples of π\pi.
    Level 3 · 4 marksTry it
  5. 5
    Solve cos⁡2x+cos⁡x+1=0\cos 2x + \cos x + 1 = 0 for 0≤x≤2π0 \le x \le 2\pi, giving your answers as exact multiples of π\pi.
    Level 3 · 4 marksTry it

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