Solve the equation 3 sinx + 4 cosx = 0 for 0° < x < 360°.

Mark scheme

Marking points from the official mark scheme (May/June 2011). The mark or mark type is shown in brackets.

1. [1] (i) tanx = -4/3
2. [1] (i) Reference angle 53.1°
3. [1] (i) x = 126.9°
4. [1] (i) x = 306.9°
5. [1] (i) Correct steps to obtain the angles
6. [1] (ii) 6 cosy + 6/cosy = 13
7. [1] (ii) Forms quadratic in cosy (6cos²y – 13cosy + 6 = 0)
8. [1] (ii) Solve 3 term quadratic
9. [1] (ii) 48.2°
10. [1] (ii) 311.8°
11. [1] (iii) 2z-3 = 0.775 (principal value of arcsin(0.7))
12. [1] (iii) 2z-3 = π - 0.775 = 2.366 (second value)
13. [1] (iii) 1.89 and 2.68