| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Standard trigonometric equations |
| Type | Convert to quadratic in tan |
| Difficulty | Standard +0.8 This question requires using the Pythagorean identity tan²θ + 1 = sec²θ to transform the equation into sec²θ - secθ = 0, then solving a quadratic in secθ and carefully handling the restricted domain including where secθ is undefined. The multiple steps, identity manipulation, and need to check validity of solutions (especially rejecting secθ = 0) make this moderately harder than a standard C3 trigonometric equation. |
| Spec | 1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals |
Find all values of $\theta$ in the interval $-180 < \theta < 180$ for which
$$\tan^2 \theta^\circ + \sec \theta^\circ = 1.$$ [6]
\hfill \mbox{\textit{OCR C3 Q3 [6]}}