| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Standard trigonometric equations |
| Type | Simple double angle equations (direct substitution) |
| Difficulty | Moderate -0.3 Part (a) is a straightforward algebraic manipulation (dividing by cos 2θ) worth 1 mark. Part (b) requires solving tan 2θ = 0.5 using a calculator, then finding all solutions in the given range by adding 180° to the principal value - a standard procedure for C2 trigonometry. The question tests routine application of trigonometric identities and solving equations with no novel insight required, making it slightly easier than average. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o 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 Q2 [6]}}