Given that θ is small and measured in radians, use the small angle approximations to show that (cos(3θ) - 1)/(θ sin(2θ)) ≈ -9/4.

Mark scheme

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

1. B1: for using the approximation cos(3θ) ≈ 1 - ((3θ)²)/(2!) = 1 - (9θ²)/2.
2. B1: for using the approximation sin(2θ) ≈ 2θ.
3. M1: for substituting all approximations into the given expression.
4. ((1 - (9θ²)/2) - 1)/(θ (2θ))
5. A1: for correct algebraic simplification of the numerator and denominator to (-(9θ²)/2)/(2θ²).
6. A1: for the final correct answer -9/4 clearly shown.