CIE A Level Maths: Pure 1

Revision Notes

3.4.3 Quadratic Trigonometric Equations

Test Yourself

Quadratic Trigonometric Equations

Solving quadratic trigonometric equations

  • If an equation involves sin2θ or cos2θ then it is a quadratic trigonometric equation
  • These can be solved by factorising and/or using trigonometric identities (see Trigonometry – Simple Identities)
  • As a quadratic can result in two solutions, will need to consider whether each solution exists and then find all solutions within a given interval for each
  • You may be asked to use degrees or radians to solve trigonometric equations
    • Make sure your calculator is in the correct mode
    • Remember common angles
      • 90° is ½π radians
      • 180° is π radians
      • 270° is 3π/2 radians
      • 360° is 2π radians

Quadratic Trigonometric Equations Diagram 1, A Level & AS Level Pure Maths Revision Notes

Exam Tip

  • Sketch the appropriate sin, cos, tan graph to ensure you find ALL solutions within the given interval, and be super-careful if you get a negative solution but have a positive interval.
  • For example, for an equation, in the interval 0° ≤ x ≤ 360°, with solution sin x = ‑¼ then sin‑1(‑¼) = -14.5 (to 1d.p.), which is not between 0 and 360 – by sketching the graph you’ll be able to spot the two solutions will be 180 + 14.5 and 360 ‑ 14.5.

Worked example

Quadratic Trigonometric Equations Example Solution, A Level & AS Level Pure Maths Revision Notes

You've read 0 of your 0 free revision notes

Get unlimited access

to absolutely everything:

  • Downloadable PDFs
  • Unlimited Revision Notes
  • Topic Questions
  • Past Papers
  • Model Answers
  • Videos (Maths and Science)

Join the 80,663 Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Did this page help you?

Lucy

Author: Lucy

Lucy has been a passionate Maths teacher for over 12 years, teaching maths across the UK and abroad helping to engage, interest and develop confidence in the subject at all levels. Working as a Head of Department and then Director of Maths, Lucy has advised schools and academy trusts in both Scotland and the East Midlands, where her role was to support and coach teachers to improve Maths teaching for all. Lucy has created revision content for a variety of domestic and international Exam Boards including Edexcel, AQA, OCR, CIE and IB.