Moderate -0.3 This is a straightforward compound angle question requiring expansion of cos(θ+60°) using the addition formula, rearranging to form a single trigonometric equation (likely tan θ = constant), then finding solutions in a given range. It's slightly easier than average as it follows a standard template with no conceptual surprises, though it does require careful algebraic manipulation and knowledge of the CAST diagram.
Attempt use of \(\cos(A + B)\) formula to obtain an equation in \(\cos \theta\) and \(\sin \theta\)
M1
Use trig formula to obtain an equation in \(\tan \theta\) (or \(\cos \theta\), \(\sin \theta\) or \(\cot \theta\))
M1
Obtain \(\tan \theta = 1/(4 + \sqrt{3})\) or equivalent (or find \(\cos \theta\), \(\sin \theta\) or \(\cot \theta\))
A1
Obtain answer \(\theta = 9.9°\)
A1
Obtain \(\theta = 189.9°\), and no others in the given interval
A1
[5 marks total]
[Ignore answers outside the given interval. Treat answers in radians as a misread (0.173, 3.31).]
[The other solution methods are via \(\cos \theta = \pm(4 + \sqrt{3})\sqrt{1 + (4 + \sqrt{3})^2}\) or \(\sin \theta = \pm 1/\sqrt{1 + (4 + \sqrt{3})^2}\).]
Attempt use of $\cos(A + B)$ formula to obtain an equation in $\cos \theta$ and $\sin \theta$ | M1 |
Use trig formula to obtain an equation in $\tan \theta$ (or $\cos \theta$, $\sin \theta$ or $\cot \theta$) | M1 |
Obtain $\tan \theta = 1/(4 + \sqrt{3})$ or equivalent (or find $\cos \theta$, $\sin \theta$ or $\cot \theta$) | A1 |
Obtain answer $\theta = 9.9°$ | A1 |
Obtain $\theta = 189.9°$, and no others in the given interval | A1 |
[5 marks total]
[Ignore answers outside the given interval. Treat answers in radians as a misread (0.173, 3.31).]
[The other solution methods are via $\cos \theta = \pm(4 + \sqrt{3})\sqrt{1 + (4 + \sqrt{3})^2}$ or $\sin \theta = \pm 1/\sqrt{1 + (4 + \sqrt{3})^2}$.]