June 2023 Paper 2 Q18
18 Here is a sketch of \(\quad y = \cos x \quad\) for values of \(x\) from \(0^\circ\) to \(360^\circ\)
\(\alpha\) is an obtuse angle measured in degrees.
\(\cos \alpha = -k \quad\) where \(k\) is a positive constant.
(a) Tick (✓) two boxes that show expressions for \(x\) where \(\quad \cos x = -k\) [2 marks]
| \(180^\circ - \alpha\) | \(180^\circ + \alpha\) | ||
| \(270^\circ - \alpha\) | \(270^\circ + \alpha\) | ||
| \(360^\circ - \alpha\) | \(360^\circ + \alpha\) |
(b) Circle the expression for \(x\) where \(\quad \sin x = -k\) [1 mark]
- \(\alpha\)
- \(90^\circ + \alpha\)
- \(180^\circ - \alpha\)
- \(180^\circ + \alpha\)
| Answer | Mark | Comments |
|---|---|---|
| \(360^\circ - \alpha\) and \(360^\circ + \alpha\) with no other answers | B2 | B1 \(360^\circ - \alpha\) or \(360^\circ + \alpha\) with at most one other answer |
Additional guidance
| Allow any unambiguous indication eg crosses in the two correct boxes with all other boxes blank | B2 |
| Mix of ticks and crosses – mark the ticks eg ticks only in the two correct boxes with crosses in some or all the other boxes | B2 |
| A tick in one of the two correct boxes with crosses in some or all the other boxes | B1 |
| Marks cannot be awarded from the diagram |
| Answer | Mark | Comments |
|---|---|---|
| \(90^\circ + \alpha\) | B1 |