O-LevelAdditional MathematicsTrigonometry4037/22 · Oct/Nov 2011 · Q25 Marks
On the grid below, draw on the same axes, for 0° ≤ x ≤ 180°, the graphs of y = sinx and y = 1 + cos 2x. [Figure 2.1]
- (i)On the grid below, draw on the same axes, for 0° ≤ x ≤ 180°, the graphs of y = sinx and y = 1 + cos 2x. [Figure 2.1][3]
- (ii)State the number of roots of the equation sinx = 1 + cos 2x for 0° ≤ x ≤ 180°.[1]
- (iii)Without extending your graphs state the number of roots of the equation sinx = 1 + cos 2x for 0° ≤ x ≤ 360°.[1]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.
- [B1] (i) Sine curve through (0, 0), (90, 1)(180, 0)
- [M1] (i) Cosine curve
- [A1] (i) through (0, 2), (45, 1), (90, 0), (135, 1), (180, 2)
- [B1√] (ii) 2
- [B1√] (iii) 2
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