| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Standard trigonometric equations |
| Type | Convert to quadratic in sin/cos |
| Difficulty | Standard +0.3 This is a trigonometric equation requiring the Pythagorean identity (sin²θ + cos²θ = 1) to convert to a quadratic in cos θ, then solving the quadratic and finding angles in the full range. It's slightly above average difficulty due to the algebraic manipulation and finding all solutions in 360°, but remains a standard C2 exercise with clear steps. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals |
Find, in degrees, the value of $\theta$ in the interval $0 \leq \theta < 360°$ for which
$$2\cos^2 \theta - \cos \theta - 1 = \sin^2 \theta$$
Give your answers to 1 decimal place where appropriate. [8]
\hfill \mbox{\textit{Edexcel C2 Q5 [8]}}