Moderate -0.3 This is a straightforward reciprocal trig equation requiring conversion to sin/cos (giving 1/cos θ = 5/sin θ, then sin θ = 5cos θ, tan θ = 5), followed by calculator use to find angles in the specified range. It's slightly easier than average as it's a direct application of definitions with minimal algebraic manipulation and standard quadrant work.
Use \(\sec\theta = \frac{1}{\cos\theta}\) and \(\cosec\theta = \frac{1}{\sin\theta}\) or other appropriate identities
B1
Must be using \(\sec^2\theta = 1 + \tan^2\theta\) and \(\cosec^2\theta = 1 + \cot^2\theta\)
Obtain \(\tan\theta = k\) using correct identities
M1
OE For any non-zero constant \(k\), if using other identities, must come from a 3-term quadratic equation
Obtain \(\tan\theta = 5\) and hence \(78.7°\)
A1
AWRT
Obtain \(258.7°\) and no other solutions in the range
A1
AWRT
Total
4
**Question 1:**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Use $\sec\theta = \frac{1}{\cos\theta}$ and $\cosec\theta = \frac{1}{\sin\theta}$ or other appropriate identities | **B1** | Must be using $\sec^2\theta = 1 + \tan^2\theta$ and $\cosec^2\theta = 1 + \cot^2\theta$ |
| Obtain $\tan\theta = k$ using correct identities | **M1** | OE For any non-zero constant $k$, if using other identities, must come from a 3-term quadratic equation |
| Obtain $\tan\theta = 5$ and hence $78.7°$ | **A1** | AWRT |
| Obtain $258.7°$ and no other solutions in the range | **A1** | AWRT |
| **Total** | **4** | |
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