Standard +0.8 This question requires converting reciprocal trig functions to standard form, applying the double angle formula for sin 2θ, then algebraic manipulation to reach a factorisable equation. While systematic, it demands fluency with multiple identities and careful algebraic handling across several steps, placing it moderately above average difficulty.
Solve a 3-term quadratic and obtain a value of \(\theta\)
M1
Obtain answer, e.g. \(201.5°\)
A1
Obtain second answer, e.g. \(338.5°\), and no others in the given interval
A1
[6]
Note: [Ignore answers outside the given interval. Treat answers in radians (3.52, 5.91) as a misread and deduct A1 from the marks for the angles.]
| Use trig formulae to express equation in terms of $\cos\theta$ and $\sin\theta$ | M1 | |
| Use Pythagoras to obtain an equation in $\sin\theta$ | M1 | |
| Obtain 3-term quadratic $2\sin^2\theta - 2\sin\theta - 1 = 0$, or equivalent | A1 | |
| Solve a 3-term quadratic and obtain a value of $\theta$ | M1 | |
| Obtain answer, e.g. $201.5°$ | A1 | |
| Obtain second answer, e.g. $338.5°$, and no others in the given interval | A1 | [6] |
**Note:** [Ignore answers outside the given interval. Treat answers in radians (3.52, 5.91) as a misread and deduct A1 from the marks for the angles.]
---