June 2023 Paper 3 Q1
1 In this question you must show detailed reasoning.
The obtuse angle \(\theta\) is such that \(\sin\theta = \dfrac{2}{\sqrt{13}}\).
Find the exact value of \(\cos\theta\). [3]
| Scheme | Marks | AO |
|---|---|---|
| DR \(\dfrac{4}{13} + \cos^2\theta = 1\) oe | M1 | 1.1a |
| \(\cos^2\theta = \dfrac{9}{13}\) | A1 | 1.1 |
| \(\cos\theta = -\dfrac{3}{\sqrt{13}}\) | A1 | 2.2a |
| [3] |
Notes
M1: M0 if decimal angles (d, r, g) seen unless superceded by correct method
A1: OR \(\cos\theta = -\dfrac{3\sqrt{13}}{13}\)
If decimals seen (as check) isw
Alternative method
| Scheme | Marks |
|---|---|
| \(13 = 4 + a^2\) or correct triangle \(\left(2,\ 3,\ \sqrt{13}\right)\) seen | M1 |
| \(a = (\pm)3\) soi | A1 |
| \(\cos\theta = -\dfrac{3}{\sqrt{13}}\) | A1 |