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Solving trigonometric equationsAQA A-Level Maths: Flashcards

What these 13 flashcards ask

  • For \sin x=k, if the principal value is \alpha, what is the second solution in 0^\circ\le x\le360^\circ?
  • For \cos x=k, if the principal value is \alpha, what is the second solution in 0^\circ\le x\le360^\circ?
  • For \tan x=k, if the principal value is \alpha, what is the second solution in 0^\circ\le x\le360^\circ?
  • Solve \tan x=-1 for 0^\circ\le x\le360^\circ.
  • Solve \cos x=-\frac12 for 0\le x\le2\pi.
  • Why does \cos x=3 have no solutions?
  • How do you solve \sin2x=k for 0^\circ\le x\le180^\circ?
  • Range for 3x-30^\circ when 0^\circ\le x\le180^\circ?
  • How many solutions does \sin2x=k (0<k<1) have for 0^\circ\le x\le360^\circ?
  • How do you solve 2\sin^2\theta+\sin\theta-1=0?
  • Which identity turns \sin^2x into a function of \cos x?
  • Why not divide \tan x=3\sin x through by \sin x?
  • Solve \sin x=-0.6 for 0^\circ\le x\le360^\circ.

Exam questions on Solving trigonometric equations

  1. In this question, xx is in degrees and 0∘≤x≤360∘0^\circ\le x\le360^\circ.
    Solve sin⁡x=−0.6\sin x=-0.6, giving your answers to 1 decimal place.2 marks
  2. Consider the equation 2sin⁡2θ+sin⁡θ−1=02\sin^2\theta+\sin\theta-1=0, where θ\theta is in degrees.
    Solve the equation for 0∘≤θ≤360∘0^\circ\le\theta\le360^\circ.2 marks
  3. In this question, xx is measured in degrees.
    Solve sin⁡2x=32\sin2x=\frac{\sqrt3}{2} for 0∘≤x≤180∘0^\circ\le x\le180^\circ.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).