June 2023 Paper 1 Q12
12
(a) Write down the value of \(x\) for \(\quad 0^\circ \leqslant x \leqslant 360^\circ \quad\) when \(\quad \sin x = -1\) [1 mark]
(b) Work out the values of \(y\) for \(\quad 0^\circ \leqslant y \leqslant 360^\circ \quad\) when \(\quad \sqrt{3}\tan y = 1\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| (\(x =\)) \(270^\circ\) | B1 |
Additional guidance
| Do not accept answers outside of the given range or a choice of answers | |
| Condone \(^\circ\) missing |
| Answer | Mark | Comments |
|---|---|---|
| \(\tan y = \dfrac{1}{\sqrt{3}}\) or \(\tan y = \dfrac{\sqrt{3}}{3}\) or \(y = \tan^{-1}\dfrac{\sqrt{3}}{3}\) or \(y = \tan^{-1}\dfrac{1}{\sqrt{3}}\) | M1 | |
| (\(y =\)) \(30^\circ\) or \(210^\circ\) | M1dep | could include up to two further incorrect values or \(30^\circ\) may be seen as part of a further calculation or on a diagram or embedded in \(\tan 30^\circ\) \(\tan 30^\circ\) embedded in a table with other exact trigonometric values (and not identified) would not gain M1dep |
| (\(y =\)) \(30^\circ\) and \(210^\circ\) | A1 |
Additional guidance
| Correct answer could come from incorrect working | M0 A0 |
| \(30^\circ\) with no working | M2 |
| \(30^\circ\) and \(210^\circ\) with no working | M2 A1 |