| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2012 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Quadratic trigonometric equations |
| Type | Show then solve: sin²/cos² substitution |
| Difficulty | Moderate -0.8 This is a straightforward C2 trigonometric equation requiring routine application of cos²θ = 1 - sin²θ to convert to a quadratic, then factorising or using the quadratic formula. The 'show that' part is mechanical substitution, and solving the resulting quadratic in sin θ is standard bookwork with no novel insight required. Easier than average A-level questions. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals |
Show that the equation $4 \cos^2 \theta = 1 + \sin \theta$ can be expressed as $4 \sin^2 \theta + \sin \theta - 3 = 0$.
Hence solve the equation for $0° \leq \theta \leq 360°$. [5]8 Show that the equation $4 \cos ^ { 2 } \theta = 1 + \sin \theta$ can be expressed as
$$4 \sin ^ { 2 } \theta + \sin \theta - 3 = 0 .$$
Hence solve the equation for $0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }$.
\hfill \mbox{\textit{OCR MEI C2 2012 Q8 [5]}}