Solve, for 0 ≤ θ < 360^(°), the equation 4 sin²θ = 5 - 4 cosθ

Mark scheme

Marking points from the official mark scheme. The mark or mark type is shown in brackets.

1. M1 for using sin²θ = 1 - cos²θ to form an equation in terms of cosθ only
2. A1 for 4(1 - cos²θ) = 5 - 4 cosθ ⇒ 4 - 4 cos²θ = 5 - 4 cosθ
3. M1 for rearranging into a 3-term quadratic equation, e.g., 4 cos²θ - 4 cosθ + 1 = 0
4. M1 for attempting to solve the quadratic for cosθ (e.g., by factorising, quadratic formula)
5. A1 for cosθ = 1/2 (only one solution for cosθ)
6. M1 for finding the principal value θ = 60^(°) and using the cosine graph/CAST diagram to find other solutions in the range.
7. A1 for θ = 60^(°), 300^(°) (and no others within the range)