| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2009 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Reciprocal Trig & Identities |
| Type | Express in terms of one function |
| Difficulty | Moderate -0.3 This is a straightforward two-part question requiring standard identity substitutions (tan²θ = sec²θ - 1, 1/cosθ = secθ) followed by solving a quadratic equation in secθ. The techniques are routine for C3 level with no novel problem-solving required, making it slightly easier than average but not trivial due to the algebraic manipulation and solving in a specified range. |
| Spec | 1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^21.05o Trigonometric equations: solve in given intervals |
3 (i) Express $2 \tan ^ { 2 } \theta - \frac { 1 } { \cos \theta }$ in terms of $\sec \theta$.\\
(ii) Hence solve, for $0 ^ { \circ } < \theta < 360 ^ { \circ }$, the equation
$$2 \tan ^ { 2 } \theta - \frac { 1 } { \cos \theta } = 4$$
\hfill \mbox{\textit{OCR C3 2009 Q3 [7]}}