Moderate -0.3 This is a straightforward application of the compound angle formula for sine, followed by algebraic manipulation using the cosecant definition. The question explicitly tells students to expand sin(θ+30°), removing any problem-solving element. Once expanded and simplified using cosec θ = 1/sin θ, it reduces to a standard linear trigonometric equation. Slightly easier than average due to the guided approach and routine techniques.
Express \(\sin(\theta + 30)\) as \(\sin\theta\cos30 + \cos\theta\sin30\)
B1
Use \(\cosec\theta = \dfrac{1}{\sin\theta}\)
B1
SOI
Correctly obtain a linear equation in \(\tan\theta\) or \(\cot\theta\)
M1
Allow unsimplified
Obtain \(\tan\theta = \dfrac{1}{4-\sqrt{3}}\), \(\dfrac{4+\sqrt{3}}{13}\), \(\dfrac{1}{2.26795...}\) or \(0.440...\)
A1
OE; May be implied by a correct answer
Obtain \(23.8\)
A1
AWRT, e.g. \(23.793...\)
Obtain \(203.8\)
A1 FT
AWRT; following *their* first value and no other solutions within the range
## Question 2:
| Answer | Mark | Guidance |
|--------|------|----------|
| Express $\sin(\theta + 30)$ as $\sin\theta\cos30 + \cos\theta\sin30$ | B1 | |
| Use $\cosec\theta = \dfrac{1}{\sin\theta}$ | B1 | SOI |
| Correctly obtain a linear equation in $\tan\theta$ or $\cot\theta$ | M1 | Allow unsimplified |
| Obtain $\tan\theta = \dfrac{1}{4-\sqrt{3}}$, $\dfrac{4+\sqrt{3}}{13}$, $\dfrac{1}{2.26795...}$ or $0.440...$ | A1 | OE; May be implied by a correct answer |
| Obtain $23.8$ | A1 | AWRT, e.g. $23.793...$ |
| Obtain $203.8$ | A1 FT | AWRT; following *their* first value and no other solutions within the range |
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