| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2020 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Standard trigonometric equations |
| Type | Quadratic in sin²/cos²/tan² |
| Difficulty | Standard +0.3 This is a quadratic-in-disguise trigonometric equation requiring substitution of u = sin²φ, solving 3u² + u - 4 = 0, then finding φ values. Slightly easier than average as it's a standard technique with straightforward algebra, though students must recognize sin²φ = 1 as the only valid solution and correctly identify all four angles in [0, 2π). |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals |
In this question you must show detailed reasoning.
Solve the equation $3\sin^4 \phi + \sin^2 \phi = 4$, for $0 \leq \phi < 2\pi$, where $\phi$ is measured in radians. [5]
\hfill \mbox{\textit{OCR H240/02 2020 Q4 [5]}}