Exact Trig & Graphs: WJEC GCSE Higher June 2018 Unit 1 Q18

Higher June 2018 Unit 1 Q18

WJECHigherCurrent spec6 marksExact Trig & Graphs Graphical Transformations

18. The following diagram shows a sketch of \(y = \cos x\) for values of \(x\) from 0° to 360°.

Graph of y = cos x from 0° to 360°, with 1, 0 and -1 marked on the y-axis and 90°, 180°, 270°, 360° on the x-axis

(a) Given that \(\cos 21^\circ = 0{\cdot}9336\), correct to 4 decimal places, write down all the solutions of the equation\[\cos x = -\,0{\cdot}9336\]

for values of \(x\) from 0° to 360°. [2]

(b)

(i) Use the following axes to sketch the graph of \(y = 2\cos x\) for values of \(x\) from 0° to 360°.
You must indicate any important points on both axes. [2]

Blank axes with origin O and 90°, 180°, 270°, 360° marked on the x-axis

(ii) Use the following axes to sketch the graph of \(y = \cos x - 1\) for values of \(x\) from 0° to 360°.
You must indicate any important points on both axes. [2]

Mark scheme (a)

Scheme	Marks	Comments
159° and 201° with no other values	B2	B1 for either angle. Check diagram. Penalise -1 for each extra value (beyond 2 attempts). Ignore extra (correct) values outside the required range.

Mark scheme (b)

Scheme	Marks	Comments
18. (b) (i) Vertical enlargement upwards and downwards	B1	Mark clear intention. Must be the correct shape, i.e. a single cycle of a cosine curve, with x-intercepts at x = 90°and x = 270°, minimum at x = 180°, maxima at x = 0 and x = 360°.
Scale factor of 2	B1	Accept any clear indication. Must have correct x and y-intercepts, correct minimum and correct point for x = 360°.
18. (b) (ii) Vertical translation	B1	Mark clear intention. Must be the correct shape, i.e. a single cycle of a cosine curve, with x-intercepts at x = 0°and x = 360°, minimum at x = 180°, maxima at x = 0 and x = 360°.
Vertical –1	B1	Accept any clear indication. Must have correct x and y-intercepts, correct minimum and correct point for x = 360°. Award SC1 for a fully labelled sketch of y = cos x + 1.