| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Exact trigonometric values |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question testing standard techniques: (i) uses Pythagorean identity to find cos from sin, (ii) applies cosine rule with exact values, (iii) uses sine rule for a numerical angle. All steps are routine C2 procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05g Exact trigonometric values: for standard angles1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=1 |
4.
The diagram shows triangle $P Q R$ in which $P Q = 7$ and $P R = 3 \sqrt { 5 }$.\\
Given that $\sin ( \angle Q P R ) = \frac { 2 } { 3 }$ and that $\angle Q P R$ is acute,\\
(i) find the exact value of $\cos ( \angle Q P R )$ in its simplest form,\\
(ii) show that $Q R = 2 \sqrt { 6 }$,\\
(iii) find $\angle P Q R$ in degrees to 1 decimal place.\\
\hfill \mbox{\textit{OCR C2 Q4 [7]}}