| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2007 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Exact trigonometric values |
| Difficulty | Moderate -0.8 This is a straightforward application of the cosine rule to find cos A, followed by using the Pythagorean identity sin²A + cos²A = 1. Both parts require only direct formula application with no problem-solving insight, making it easier than average but not trivial since it requires exact value manipulation. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| (a) \(4^2 = 5^2 + 6^2 - (2\times5\times6\cos\theta)\) | M1 | Also scored for equivalent rearrangements |
| \(\cos\theta = \dfrac{5^2+6^2-4^2}{2\times5\times6}\) | A1 | Rearranged correctly and numerically correct |
| \(= \dfrac{45}{60} = \dfrac{3}{4}\) | A1cso | |
| (b) \(\sin^2 A + \left(\dfrac{3}{4}\right)^2 = 1\) | M1 | Or equivalent Pythagorean method |
| \(\sin^2 A = \dfrac{7}{16},\quad \sin A = \dfrac{1}{4}\sqrt{7}\) | A1 | Or exact equivalents e.g. \(\sqrt{\dfrac{7}{16}}\), \(\sqrt{0.4375}\) |
# Question 4:
| Answer/Working | Marks | Guidance |
|---|---|---|
| **(a)** $4^2 = 5^2 + 6^2 - (2\times5\times6\cos\theta)$ | M1 | Also scored for equivalent rearrangements |
| $\cos\theta = \dfrac{5^2+6^2-4^2}{2\times5\times6}$ | A1 | Rearranged correctly and numerically correct |
| $= \dfrac{45}{60} = \dfrac{3}{4}$ | A1cso | |
| **(b)** $\sin^2 A + \left(\dfrac{3}{4}\right)^2 = 1$ | M1 | Or equivalent Pythagorean method |
| $\sin^2 A = \dfrac{7}{16},\quad \sin A = \dfrac{1}{4}\sqrt{7}$ | A1 | Or exact equivalents e.g. $\sqrt{\dfrac{7}{16}}$, $\sqrt{0.4375}$ |
**Total: 5 marks**
---4.
Figure 1
Figure 1 shows the triangle $A B C$, with $A B = 6 \mathrm {~cm} , B C = 4 \mathrm {~cm}$ and $C A = 5 \mathrm {~cm}$.
\begin{enumerate}[label=(\alph*)]
\item Show that $\cos A = \frac { 3 } { 4 }$.
\item Hence, or otherwise, find the exact value of $\sin A$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 2007 Q4 [5]}}