| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Addition & Double Angle Formulae |
| Type | Solve equation with sin2x/cos2x by substitution |
| Difficulty | Standard +0.3 Part (i) is straightforward inverse tan manipulation requiring one algebraic step. Part (ii) uses the standard double angle formula cos(2θ) = 1 - 2sin²θ to convert to a quadratic in sin θ, then solving within a given range. Both are routine C3 techniques with no novel insight required, making this slightly easier than average. |
| Spec | 1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}
\item (i) Find the exact value of $x$ such that
\end{enumerate}
$$3 \tan ^ { - 1 } ( x - 2 ) + \pi = 0$$
(ii) Solve, for $- \pi < \theta < \pi$, the equation
$$\cos 2 \theta - \sin \theta - 1 = 0$$
giving your answers in terms of $\pi$.\\
\hfill \mbox{\textit{OCR C3 Q5 [8]}}