| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Standard trigonometric equations |
| Type | Convert to quadratic in sin/cos |
| Difficulty | Moderate -0.3 This is a standard C2 trigonometric equation requiring the identity cos²x = 1 - sin²x to convert to a quadratic in sin x, then factorization or quadratic formula, followed by routine inverse trig. Part (a) is guided algebraic manipulation (2 marks), and part (b) is straightforward solving with standard angle finding. Slightly easier than average due to the scaffolding and being a textbook-style question with no novel insight required. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}[label=(\alph*)]
\item Show that the equation
$$5 \cos^2 x = 3(1 + \sin x)$$
can be written as
$$5 \sin^2 x + 3 \sin x - 2 = 0.$$
[2]
\item Hence solve, for $0 \leq x < 360°$, the equation
$$5 \cos^2 x = 3(1 + \sin x),$$
giving your answers to 1 decimal place where appropriate.
[5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q4 [7]}}