| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 4 |
| Topic | Standard trigonometric equations |
| Type | Double angle equations requiring identity expansion and factorisation |
| Difficulty | Standard +0.8 This requires applying the double angle formula (sin 2x = 2sin x cos x), algebraic manipulation to form a quadratic in sin x, and solving while rejecting invalid solutions. It's above average difficulty due to the multi-step algebraic reasoning and need to handle the quadratic carefully, but it's a standard trigonometric equation type for A-level. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
In this question you must show detailed reasoning.
Given that $5\sin 2x = 3\cos x$, where $0° < x < 90°$, find the exact value of $\sin x$. [4]
\hfill \mbox{\textit{OCR H240/03 2017 Q3 [4]}}