| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2010 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Quadratic trigonometric equations |
| Type | Show then solve: sin²/cos² substitution |
| Difficulty | Moderate -0.3 This is a standard C2 trigonometric equation requiring the identity sin²x + cos²x = 1 to convert to a quadratic in cos x, then solving using the quadratic formula or factorization. The 'show that' part is routine algebraic manipulation, and solving quadratics in trig functions is a core C2 skill. Slightly easier than average due to the guided structure and straightforward factorization (2cos x - 1)(cos x + 3) = 0. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals |
1 (i) Show that the equation
$$2 \sin ^ { 2 } x = 5 \cos x - 1$$
can be expressed in the form
$$2 \cos ^ { 2 } x + 5 \cos x - 3 = 0$$
(ii) Hence solve the equation
$$2 \sin ^ { 2 } x = 5 \cos x - 1$$
giving all values of $x$ between $0 ^ { \circ }$ and $360 ^ { \circ }$.
\hfill \mbox{\textit{OCR C2 2010 Q1 [6]}}