| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Reciprocal Trig & Identities |
| Type | Solve equation with reciprocal functions |
| Difficulty | Standard +0.8 This question requires converting cosec to 1/sin, forming a quadratic in sin θ or cos θ, solving it, and finding solutions in a restricted domain. It combines reciprocal trig functions with equation solving and requires careful algebraic manipulation, making it moderately challenging but still within standard C3 scope. |
| Spec | 1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{3}{\sin\theta} = -8\cos\theta\) | M1 | |
| \(3 = -8\sin\theta\cos\theta = -4\sin 2\theta\) | M1 | |
| \(\sin 2\theta = -\frac{3}{4}\) | A1 | |
| \(2\theta = 180 + 48.590, 360 - 48.590 = 228.590, 311.410\) | M1 | |
| \(\theta = 114.3, 155.7\) (1dp) | A2 | (6) |
$\frac{3}{\sin\theta} = -8\cos\theta$ | M1 |
$3 = -8\sin\theta\cos\theta = -4\sin 2\theta$ | M1 |
$\sin 2\theta = -\frac{3}{4}$ | A1 |
$2\theta = 180 + 48.590, 360 - 48.590 = 228.590, 311.410$ | M1 |
$\theta = 114.3, 155.7$ (1dp) | A2 | (6)\begin{enumerate}
\item Solve the equation
\end{enumerate}
$$3 \operatorname { cosec } \theta ^ { \circ } + 8 \cos \theta ^ { \circ } = 0$$
for $\theta$ in the interval $0 \leq \theta \leq 180$, giving your answers to 1 decimal place.\\
\hfill \mbox{\textit{Edexcel C3 Q1 [6]}}