O-LevelAdditional MathematicsTrigonometry4037/22 · May/June 2013 · Q109 Marks
The function f is defined, for 0° < x < 360°, by f(x) = 1 + 3 cos 2x.
- (a)(i)Sketch the graph of y = f(x) on the axes below.[4]
- (a)(ii)State the amplitude of f.[1]
- (a)(iii)State the period of f.[1]
- (b)Given that cos x = p, where 270° < x < 360°, find cosec x in terms of p.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.
- [B1] (a)(i) shape; cosine curve - must be approaching a turning point
- [B1] (a)(i) be centred on y = 1
- [B1] (a)(i) clear intent to have min at -2 and max at 4
- [B1] (a)(i) 2 cycles
- [B1] (a)(ii) 3
- [B1] (a)(iii) 180
- [B1] (b) cosec x = 1/sin x soi
- [B1] (b) sin x = √(1 - cos² x) or √(1 - p²)
- [B1] (b) -1 / √(1 - p²) o.e.
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