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Higher June 2022 Paper 1 Q21

EduqasHigherCurrent spec8 marksExact Trig & GraphsGraphical Transformations

21.

(a)
(i) On the axes below, sketch the graph of \(y = \cos x\) for \(-180^\circ \leqslant x \leqslant 180^\circ\). [2]
Blank axes: x axis marked −180°, −90°, 0°, 90°, 180°; y axis with no scale
(ii) Solve \(\cos x = \dfrac{\sqrt{3}}{2}\) for \(-180^\circ \leqslant x \leqslant 180^\circ\). [2]
(b) The diagram shows a sketch of the graph of \(y = f(x)\).
The point \(A\) has coordinates \((-2, 0)\) and the point \(B\) has coordinates \((0, 3)\).
Graph of y = f(x): a V shape with its vertex at A(−2, 0) on the x axis; the right branch rises to B(0, 3) on the y axis and stops; the left branch rises steeply to the left
(i) Sketch the graph of \(y = f(x) - 1\) on the axes below.
You must indicate the coordinates of the new positions of the points \(A\) and \(B\). [2]
Blank x and y axes with origin O
(ii) Sketch the graph of \(y = f(x - 3)\) on the axes below.
You must indicate the coordinates of the new positions of the points \(A\) and \(B\). [2]
Blank x and y axes with origin O
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