Standard +0.3 This question requires expanding the compound angle formula for cos(θ - 60°), substituting sec θ = 1/cos θ, and solving a resulting trigonometric equation. While it involves multiple steps and algebraic manipulation, it follows a standard procedure for this topic with no novel insight required. The technique is straightforward once the compound angle is expanded, making it slightly easier than average.
Either divide by \(\cos\theta\) to find value of \(\tan\theta\) or use another correct method to find \(\sin\theta\) or \(\cos\theta\)
M1
May still involve \(\cos 60\) and \(\sin 60\)
Obtain \(\tan\theta = \dfrac{7}{\sqrt{3}}\) or \(\tan\theta = 4.04...\) or \(\sin\theta = \dfrac{7}{\sqrt{52}}\) or \(\sin\theta = 0.970...\) or \(\cos\theta = \dfrac{\sqrt{3}}{\sqrt{52}}\) or \(\cos\theta = 0.240...\)
A1
Obtain \(-103.9\) and \(76.1\)
A1
Or greater accuracy; and no others between \(-180\) and \(180\)
Total: 5
**Question 2:**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Attempt to express equation in terms of $\cos\theta$ and $\sin\theta$ only, using a correct identity and $\sec\theta = \dfrac{1}{\cos\theta}$ | M1 | |
| Obtain $\cos\theta\cos 60 + \sin\theta\sin 60 = 4\cos\theta$ | A1 | OE |
| Either divide by $\cos\theta$ to find value of $\tan\theta$ or use another correct method to find $\sin\theta$ or $\cos\theta$ | M1 | May still involve $\cos 60$ and $\sin 60$ |
| Obtain $\tan\theta = \dfrac{7}{\sqrt{3}}$ or $\tan\theta = 4.04...$ or $\sin\theta = \dfrac{7}{\sqrt{52}}$ or $\sin\theta = 0.970...$ or $\cos\theta = \dfrac{\sqrt{3}}{\sqrt{52}}$ or $\cos\theta = 0.240...$ | A1 | |
| Obtain $-103.9$ and $76.1$ | A1 | Or greater accuracy; and no others between $-180$ and $180$ |
| | **Total: 5** | |