Standard +0.3 This is a trigonometric equation requiring factorization and substitution techniques that are standard for AS-level. Students must factor out sin θ, use tan θ = sin θ/cos θ, then solve a quadratic in sin θ. While it involves multiple steps and careful algebraic manipulation, the techniques are all routine for this level with no novel insight required. The 5-mark allocation and restricted domain make it slightly above trivial but still below average difficulty.
Solve the equation
$$\sin\theta\tan\theta + 2\sin\theta = 3\cos\theta \quad \text{where } \cos\theta \neq 0$$
Give all values of \(\theta\) to the nearest degree in the interval \(0° < \theta < 180°\)
Fully justify your answer.
[5 marks]
Solve the equation
$$\sin\theta\tan\theta + 2\sin\theta = 3\cos\theta \quad \text{where } \cos\theta \neq 0$$
Give all values of $\theta$ to the nearest degree in the interval $0° < \theta < 180°$
Fully justify your answer.
[5 marks]
\hfill \mbox{\textit{AQA AS Paper 2 Q7 [5]}}