| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Reciprocal Trig & Identities |
| Type | Sketch reciprocal function graphs |
| Difficulty | Standard +0.3 This is a straightforward application of reciprocal trig transformations. Students need to identify asymptotes where cos(x - π/6) = 0, sketch the sec curve with vertical shift +2 and horizontal shift +π/6, then solve 2 + sec(x - π/6) = 0 algebraically. While it requires understanding of sec graphs and transformations, these are standard C3 techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.05f Trigonometric function graphs: symmetries and periodicities1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}
\item (i) Sketch the graph of $y = 2 + \sec \left( x - \frac { \pi } { 6 } \right)$ for $x$ in the interval $0 \leq x \leq 2 \pi$.
\end{enumerate}
Show on your sketch the coordinates of any turning points and the equations of any asymptotes.\\
(ii) Find, in terms of $\pi$, the $x$-coordinates of the points where the graph crosses the $x$-axis.\\
\hfill \mbox{\textit{OCR C3 Q4 [8]}}