(a) Sketch the curve \(y = \cos x\), for values of \(x\) in the range \(x\) = 0° to \(x\) = 360°. You must indicate any important values on the axes. [2]
(b) Solve the equation \(\cos x = 0{\cdot}7\). Give all solutions in the range \(x\) = 0° to \(x\) = 360°. [2]
Mark scheme (a)
Scheme
Marks
Comments
General cosine curve with appropriate orientation and position.
M1
Ignore curve shown for values x< 0° or x> 360°.
Correct sketch with curve passing through (0°,1), (90°,0) and (270°,0) and approximately (180°,-1) and (360°,1) AND 90(°), 180(°), 270(°), 360(°) indicated on the x-axis AND -1 and 1 indicated on the y-axis.
A1
Accept 180° as mid-way between 0° and 360° if unlabelled. Accept 360° as unlabelled provided the sketch does not exceed 360°.
Mark scheme (b)
Scheme
Marks
Comments
46(°) AND 314(°) OR 45·6(°) AND 314·4(°) OR 45·57(29…°) AND 314·4(27…°).
B2
B1 for sight of one correct angle. Allow embedded answers. If more than two answers offered award B1 for sight of one correct angle.
If no marks, award SC1 for truncated answers 45(°) AND 315(°) OR 45·5(°) AND 314·5(°).
Corrected by Westie's Workshop
The board's mark scheme printed “If no marks, awarded SC1”. Changed to “If no marks, award SC1” because the instruction to the marker should read “award”, as in the other special-case lines.
Original: see the board's mark scheme PDF (link above).
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