Standard +0.3 This is a standard harmonic form question requiring compound angle expansion and R-formula technique to solve a trigonometric equation. While it involves multiple steps (expanding compound angles, converting to harmonic form, solving), these are well-practiced techniques in P2. The working is methodical rather than requiring insight, making it slightly easier than average.
Use correct process to find second value of \(\theta\)
DM1
\(\frac{180° + \textit{their } 2\theta}{2}\) or \(90° + \textit{their } \theta\); Allow if using radians correctly
Obtain \(\theta = 100.5\)
A1 FT
AWRT; and no other answers within the range
Total
6
## Question 3:
| Answer | Mark | Guidance |
|--------|------|----------|
| Expand at least one of $\sin(2\theta + 30)$ and $\cos(2\theta + 60)$ correctly | B1 | |
| Attempt expansions and division by $\cos 2\theta$ to obtain equation in $\tan 2\theta$ only | *M1 | |
| Obtain $\tan 2\theta = \frac{4}{6\sqrt{3}}, \frac{2}{3\sqrt{3}}, \frac{2\sqrt{3}}{9}$, 0.3849... | A1 | OE |
| Obtain $\theta = 10.5$ | A1 | AWRT, e.g. 10.525… A0 for 0.184 radians |
| Use correct process to find second value of $\theta$ | DM1 | $\frac{180° + \textit{their } 2\theta}{2}$ or $90° + \textit{their } \theta$; Allow if using radians correctly |
| Obtain $\theta = 100.5$ | A1 FT | AWRT; and no other answers within the range |
| **Total** | **6** | |
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