| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Proofs |
| Type | Prove Pythagorean identity from triangle |
| Difficulty | Easy -1.2 This is a straightforward proof using Pythagoras' theorem on a right-angled triangle to derive the fundamental trigonometric identity. It requires only basic recall of definitions (sin = opp/hyp, cos = adj/hyp) and one application of Pythagoras, making it easier than average. The restriction on θ values (0° < θ < 90°) is also standard. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=1 |
Use the triangle in Fig. 4 to prove that $\sin^2 \theta + \cos^2 \theta = 1$. For what values of $\theta$ is this proof valid? [3]
\includegraphics{figure_4}
\hfill \mbox{\textit{OCR MEI C3 Q5 [3]}}