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Solving trigonometric equationsEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

  • Solutions of \sin x=k in 0\le x\le360^\circ?
  • Solutions of \cos x=k in 0\le x\le360^\circ?
  • Solutions of \tan x=k in 0\le x\le360^\circ?
  • Interval for x+70^\circ if 0<x<360^\circ?
  • Interval for 2x if -180^\circ<x<180^\circ?
  • How many solutions has \sin2x=k in 0\le x<360^\circ (for 0<k<1)?
  • Solve \sin(x+70^\circ)=0.5, 0<x<360^\circ.
  • Which identity turns 6\cos^2x+\sin x-5=0 into a quadratic in \sin x?
  • Solve 6\sin^2x-\sin x-1=0, 0\le x<360^\circ.
  • How do you solve \sin x=2\cos x?
  • Why reject \sin x=2?
  • Exact solutions of \sin x=\frac{\sqrt3}{2} for 0\le x<2\pi?

Exam questions on Solving trigonometric equations

  1. The equation sin⁡(x+70∘)=0.5\sin(x+70^\circ)=0.5 is to be solved for 0<x<360∘0<x<360^\circ.
    Solve sin⁡(x+70∘)=−0.5\sin(x+70^\circ)=-0.5 for 0<x<360∘0<x<360^\circ.2 marks
  2. The equation 3+5cos⁡2x=13+5\cos2x=1 is to be solved for −180∘<x<180∘-180^\circ<x<180^\circ.
    Solve the equation, giving your answers to 1 decimal place.2 marks
  3. Consider the equation 6cos⁡2x+sin⁡x−5=06\cos^2x+\sin x-5=0 for 0≤x<360∘0\le x<360^\circ.
    Show that the equation can be written as 6sin⁡2x−sin⁡x−1=06\sin^2x-\sin x-1=0.3 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).