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Quadratic Trigonometric Equations (CIE A Level Maths: Pure 1)
Revision Note
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
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
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