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Trigonometric identitiesAQA A-Level Maths: Flashcards

What these 13 flashcards ask

  • What does \tan\theta equal in terms of \sin\theta and \cos\theta?
  • State the Pythagorean identity.
  • Rearrange the identity to give \sin^2\theta.
  • Rearrange the identity to give \cos^2\theta.
  • When is \tan\theta undefined?
  • Simplify \cos x\tan x.
  • Simplify \frac{\sin x}{\tan x}.
  • Simplify \frac{\sin^2x}{1-\sin^2x}.
  • What does \sin^2\theta mean?
  • \sin\theta=\frac{3}{5}, \theta acute: find \cos\theta and \tan\theta.
  • If \sin\theta=3\cos\theta, what is \tan\theta?
  • Which side do you start from when proving an identity?
  • Why must you check the sign after \cos\theta=\pm\sqrt{1-\sin^2\theta}?

Exam questions on Trigonometric identities

  1. The angle θ\theta is obtuse and sin⁡θ=513\sin\theta=\frac{5}{13}.
    Find the exact value of sin⁡θcos⁡θ\sin\theta\cos\theta.2 marks
  2. For all values of xx for which each expression is defined, let A=cos⁡xtan⁡xA=\cos x\tan x and B=sin⁡xtan⁡xB=\frac{\sin x}{\tan x}.
    Show that A2+B2=1A^2+B^2=1.2 marks
  3. The angle θ\theta is acute and satisfies sin⁡θ=2cos⁡θ\sin\theta=2\cos\theta.
    Find the exact value of cos⁡θ\cos\theta.3 marks
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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).