Edexcel C3 2007 January — Question 5

Exam BoardEdexcel
ModuleC3 (Core Mathematics 3)
Year2007
SessionJanuary
TopicHarmonic Form

5. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{a4ad749b-181b-4680-8771-94d9b581125a-07_865_926_301_516}
\end{figure} Figure 1 shows an oscilloscope screen. The curve shown on the screen satisfies the equation $$y = \sqrt { 3 } \cos x + \sin x$$
  1. Express the equation of the curve in the form \(y = R \sin ( x + \alpha )\), where \(R\) and \(\alpha\) are constants, \(R > 0\) and \(0 < \alpha < \frac { \pi } { 2 }\).
  2. Find the values of \(x , 0 \leqslant x < 2 \pi\), for which \(y = 1\).