| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Find coordinates of turning points |
| Difficulty | Moderate -0.8 This is a straightforward C2 trigonometry question requiring basic graph transformations (horizontal shift) and solving a simple trig equation using calculator and symmetry. Both parts are routine textbook exercises with no problem-solving insight needed, making it easier than average but not trivial since it requires understanding of phase shifts and finding multiple solutions in a given interval. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks | Guidance |
|---|---|---|
| (a)(i) [Sketch showing curve with shape roughly of \(\cos(x)\) with minimum at origin] | B2 | |
| (a)(ii) \((-60, -1), (120, 1)\) | B2 | |
| (b) \(x - 30 = -180 - 20.5, 20.5\) | B1 M1 | |
| \(x = -200.5, 20.5\) | M1 A1 | |
| \(x = -170.5, 50.5\) (1dp) | (8 marks) |
**(a)(i)** [Sketch showing curve with shape roughly of $\cos(x)$ with minimum at origin] | B2 |
**(a)(ii)** $(-60, -1), (120, 1)$ | B2 |
**(b)** $x - 30 = -180 - 20.5, 20.5$ | B1 M1 |
$x = -200.5, 20.5$ | M1 A1 |
$x = -170.5, 50.5$ (1dp) | | (8 marks)\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Sketch the curve $y = \sin (x - 30)°$ for $x$ in the interval $-180 \leq x \leq 180$.
\item Write down the coordinates of the turning points of the curve in this interval. [4]
\end{enumerate}
\item Find all values of $x$ in the interval $-180 \leq x \leq 180$ for which
$$\sin (x - 30)° = 0.35,$$
giving your answers to 1 decimal place. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q4 [8]}}