O-LevelAdditional MathematicsTrigonometry4037/11 · Oct/Nov 2011 · Q910 Marks
Solve 1 + cot² x = 8 sin x for 0° ≤ x ≤ 360°.
- (i)Solve 1 + cot² x = 8 sin x for 0° ≤ x ≤ 360°.[5]
- (ii)Solve 4 sin(2y – 0.3) + 5 cos(2y – 0.3) = 0 for 0 ≤ y ≤ π radians.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.
- [1] (i) M1 for use of correct identity or equivalent cosec² x = 8 sin x
- [1] (i) M1 for dealing with cosec or equivalent sin³ x = 1/8
- [1] (i) M1 for attempt to solve sin x = 1/2
- [2] (i) A1, A1 x = 30°, 150°
- [2] (ii) M1, A1 for attempt to get in terms of tan tan(2y - 0.3) = -5/4
- [1] (ii) M1 for dealing with order correctly 2y - 0.3 = 2.2455, 5.387
- [2] (ii) A1, A1 y = 1.27, 2.84 (allow 1.28 and 2.85)
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