Standard +0.3 This question requires expanding compound angle formulae for both sine and cosine, then solving a resulting trigonometric equation. While it involves multiple steps (expansion, simplification, rearrangement into standard form), the techniques are standard P3 material with no novel insight required. The restricted interval makes finding solutions straightforward. Slightly easier than average due to being a routine application of compound angle formulae.
Attempt use of \(\sin(A+B)\) and \(\cos(A-B)\) formulae to obtain an equation in \(\cos\theta\) and \(\sin\theta\)
M1
Obtain a correct equation in any form
A1
Use trig. formula to obtain an equation in \(\tan\theta\) (or \(\cos\theta, \sin\theta\) or \(\cot\theta\))
M1
Obtain \(\tan\theta = \frac{\sqrt{6}-1}{1-\sqrt{2}}\), or equivalent (or find \(\cos\theta, \sin\theta\) or \(\cot\theta\))
A1
Obtain answer \(\theta = 105.9°\), and no others in the given interval
A1
[Ignore answers outside the given material]
Attempt use of $\sin(A+B)$ and $\cos(A-B)$ formulae to obtain an equation in $\cos\theta$ and $\sin\theta$ | M1 |
Obtain a correct equation in any form | A1 |
Use trig. formula to obtain an equation in $\tan\theta$ (or $\cos\theta, \sin\theta$ or $\cot\theta$) | M1 |
Obtain $\tan\theta = \frac{\sqrt{6}-1}{1-\sqrt{2}}$, or equivalent (or find $\cos\theta, \sin\theta$ or $\cot\theta$) | A1 |
Obtain answer $\theta = 105.9°$, and no others in the given interval | A1 | [Ignore answers outside the given material] | [5]