Quadratic Trigonometric Equations (Edexcel IAL Maths)

Spec point — 6.2

Quadratic trigonometric equations

How do I solve 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, you 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

Exam Hint

• 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