| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Standard trigonometric equations |
| Type | Simple double angle equations (direct substitution) |
| Difficulty | Moderate -0.3 This is a straightforward C2 trigonometric equation requiring basic manipulation (dividing by cos to get tan) and solving for multiple angles in a given range. Part (a) is trivial algebraic rearrangement worth 1 mark. Part (b) requires finding all solutions of tan(2θ)=0.5 in 0≤θ<360°, which is routine application of inverse tan and the periodicity of tan, though students must remember to work with 2θ first then divide by 2. Slightly easier than average due to the guided structure and standard techniques involved. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals |
Given that $2 \sin 2\theta = \cos 2\theta$,
\begin{enumerate}[label=(\alph*)]
\item show that $\tan 2\theta = 0.5$. [1]
\item Hence find the values of $\theta$, to one decimal place, in the interval $0 \leq \theta < 360$ for which $2 \sin 2\theta ° = \cos 2\theta °$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q6 [6]}}