A-LevelMathematicsTrigonometry9709/12 · Oct/Nov 2011 · Q57 Marks
Sketch, on the same diagram, the graphs of y = sinx and y = cos 2x for 0° ≤ x ≤ 180°.
- (i)Sketch, on the same diagram, the graphs of y = sinx and y = cos 2x for 0° ≤ x ≤ 180°.[3]
- (ii)Verify that x = 30° is a root of the equation sin x = cos 2x, and state the other root of this equation for which 0° ≤ x ≤ 180°.[2]
- (iii)Hence state the set of values of x, for 0° ≤ x ≤ 180°, for which sinx < cos 2x.[2]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.
- [3] y = sinx (0,0). (π,0) + curve
- [3] y = cos2x One full cycle.
- [3] y = cos2x starts and finishes at (0, 1) and oscillates between –1 and +1.
- [2] Evidence of sin 30 = cos 60 = 0.5
- [2] Other root is 150°
- [2] 0 ≤ x < 30 and 150 < x ≤ 180
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