\begin{enumerate}
  \item (a) Write $2 \sin \theta - \cos \theta$ in the form $R \sin ( \theta - \alpha )$, where $R$ and $\alpha$ are constants, $R > 0$ and $0 < \alpha \leqslant 90 ^ { \circ }$. Give the exact value of $R$ and give the value of $\alpha$ to one decimal place.\\
(3)
\end{enumerate}

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{29b56d51-120a-4275-a761-8b8aed7bca54-32_513_1194_404_374}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}

Figure 3 shows a sketch of the graph with equation $y = 2 \sin \theta - \cos \theta , \quad 0 \leqslant \theta < 360 ^ { \circ }$\\
(b) Sketch the graph with equation

$$y = | 2 \sin \theta - \cos \theta | , \quad 0 \leqslant \theta < 360 ^ { \circ }$$

stating the coordinates of all points at which the graph meets or cuts the coordinate axes.

The temperature of a warehouse is modelled by the equation

$$f ( t ) = 5 + \left| 2 \sin ( 15 t ) ^ { \circ } - \cos ( 15 t ) ^ { \circ } \right| , \quad 0 \leqslant t < 24$$

where $\mathrm { f } ( t )$ is the temperature of the warehouse in degrees Celsius and $t$ is the time measured in hours from midnight.

State\\
(c) (i) the maximum value of $f ( t )$,\\
(ii) the largest value of $t$, for $0 \leqslant t < 24$, at which this maximum value occurs. Give your answer to one decimal place.

\hfill \mbox{\textit{Edexcel C34 2017 Q10 [9]}}