7 Given that 2+cotθ = 3x and sinθ = √y, find y in terms of x.

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

1. [3] B1 Use of cot²θ+1=cosec²θ and cosecθ = 1/sinθ or 4+cot²θ = 9x² gets B0 M0 A0 unless recovered
2. [3] M1 For use of the identity to substitute cotθ to get 2+cosθ/√y = 3x and rearranging to get y = cos²θ/(3x-2)² oe OR For use of the identity to substitute cos²θ to get y = (1-sin²θ)/(3x-2)² and use of sin²θ = y
3. [3] A1 (y = 1/(3x-2)²+1) oe