Express 0.5 cos θ – 1.2 sin θ in the form R cos(θ + α), where R > 0 and 0° < α < 90°, giving the value of α correct to 2 decimal places.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

1. [B1] State R = 1.3 or 10/3 (Not √1.69)
2. [M1] Use appropriate trigonometry to find α (AWRT ±1.18rads, AWRT ±0.391rads, AWRT ±67.4°, AWRT ±22.6°)
3. [A1] Obtain 67.38 with no errors seen (AWRT)
4. [M1] Carry out correct method to find one value of θ between 0 and 360
5. [A1] Obtain 240.6 (or 344.6)
6. [M1] Carry out correct method to find second value of θ between 0 and 360 (Must be using either degrees throughout or radians throughout for M marks)
7. [A1] Obtain 344.6 (or 240.6)
8. [M1] Recognise expression as [3 – 2Rcos(θ + α)]²
9. [A1] Obtain [3 – 2 * (-1.3)]² and hence 31.36 or 31.4
10. [A1] Obtain [3 – 2 * 1.3]² and hence 0.16