| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Harmonic Form |
| Type | Express and solve equation |
| Difficulty | Standard +0.3 This is a standard C3 harmonic form question with routine techniques. Part (i)(a) uses the standard R cos(θ+α) expansion requiring R=13, tan α=5/12. Part (i)(b) is straightforward solving after the conversion. Part (ii) requires multiplying by sin θ to get a quadratic in tan θ, which is a common C3 technique. All steps are textbook-standard with no novel insight required, making it slightly easier than average. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05n Harmonic form: a sin(x)+b cos(x) = R sin(x+alpha) etc1.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}[label=(\roman*)]
\item \begin{enumerate}[label=(\alph*)]
\item Express $(12 \cos \theta - 5 \sin \theta)$ in the form $R \cos (\theta + \alpha)$, where $R > 0$ and $0 < \alpha < 90°$. [4]
\item Hence solve the equation
$$12 \cos \theta - 5 \sin \theta = 4,$$
for $0 < \theta < 90°$, giving your answer to 1 decimal place. [3]
\end{enumerate}
\item Solve
$$8 \cot \theta - 3 \tan \theta = 2,$$
for $0 < \theta < 90°$, giving your answer to 1 decimal place. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q36 [12]}}