| Exam Board | OCR |
|---|---|
| Module | AS Pure (AS Pure Mathematics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 5 |
| Topic | Standard trigonometric equations |
| Type | Double angle equations requiring identity expansion and factorisation |
| Difficulty | Standard +0.3 This is a standard trigonometric equation requiring the identity cos²x = 1 - sin²x to convert to a quadratic in sin x, then solving and checking solutions in the given range. It's slightly above average difficulty due to the algebraic manipulation and domain restriction, but follows a well-practiced technique 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 |
In this question you must show detailed reasoning.
Solve the equation $2\cos^2 x = 2 - \sin x$ for $0° \leq x \leq 180°$. [5]
\hfill \mbox{\textit{OCR AS Pure 2017 Q2 [5]}}