O-LevelAdditional MathematicsTrigonometry4037/22 · May/June 2012 · Q915 Marks
3 sin x – 5 cos x = 0 for 0° < x < 360°,
- (a)(i)3 sin x – 5 cos x = 0 for 0° < x < 360°,[5]
- (a)(ii)5 sin² y + 9 cos y – 3 = 0 for 0° < y < 360°.[5]
- (b)Solve sin(3 – z) = 0.8 for 0 < z < π radians.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.
- [B1] (a)(i) tan x = 5/3
- [B1] (a)(i) x = 59(.0)
- [B1√] (a)(i) x = 239(.0) and no others
- [B1] (a)(ii) Use sin² y = 1 − cos² y
- [B1] (a)(ii) 5 cos² y - 9 cos y – 2 = 0
- [M1] (a)(ii) Solve 3 term quadratic (in cosy)
- [A1] (a)(ii) 101.5
- [B1√] (a)(ii) 258.5 and no others
- [B1] (b) (3-z) = 0.927 or 0.93
- [B1] (b) 2.07
- [M1] (b) (3−z) = π−0.927
- [A1] (b) 0.786 or 0.785 or 0.79 and no others
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