ASMaths: PureOCRRevision Notes5. Trigonometry5.3 Trigonometric Equations5.3.3 Quadratic Trigonometric Equations

Quadratic Trigonometric Equations (OCR AS Maths: Pure)

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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

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

Examiner 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

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    Lucy

    Author: Lucy

    Expertise: Head of STEM

    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.