Higher November 2021 Paper 1 Q28

AQACurrent spec3 marksGraphical Transformations

28 Here is the graph of \(\quad y = \cos x \quad\) for \(\ 0° \leqslant x \leqslant 360°\)

Graph of y = cos x for 0° to 360° on a grid, with y from −2 to 2

In parts (a) and (b) the graph of \(\quad y = \cos x \quad\) is shown as a dashed line.

(a) On the grid below, draw the graph of \(\quad y = \cos(x - 90°) \quad\) for \(\ 0° \leqslant x \leqslant 360°\) [1 mark]
Grid with y = cos x drawn dashed for 0° to 360°
(b) On the grid below, draw the graph of \(\quad y = 1 + \cos x \quad\) for \(\ 0° \leqslant x \leqslant 360°\) [1 mark]
Grid with y = cos x drawn dashed for 0° to 360°
(c) Rita tries to draw the graph of \(\quad y = \cos(-x) \quad\) for \(\ 0° \leqslant x \leqslant 360°\)

Here is her graph.

Rita’s graph: a curve starting at (0, −1), rising to 1 at 180° and back to −1 at 360°

Give a reason why Rita’s graph is incorrect. [1 mark]

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