SPS SPS SM Pure 2021 June — Question 9

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2021
SessionJune
TopicTrig Equations

9. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{106e8e6b-912d-45ef-89e9-12ffc04bfd25-14_895_1337_207_468} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows part of the curve with equation \(y = 3 \cos x ^ { \circ }\).
The point \(P ( c , d )\) is a minimum point on the curve with \(c\) being the smallest negative value of \(x\) at which a minimum occurs.
  1. State the value of \(c\) and the value of \(d\).
  2. State the coordinates of the point to which \(P\) is mapped by the transformation which transforms the curve with equation \(y = 3 \cos x ^ { \circ }\) to the curve with equation
    1. \(y = 3 \cos \left( \frac { x ^ { \circ } } { 4 } \right)\)
    2. \(y = 3 \cos ( x - 36 ) ^ { \circ }\)
  3. Solve, for \(450 ^ { \circ } \leqslant \theta < 720 ^ { \circ }\), $$3 \cos \theta = 8 \tan \theta$$ giving your solution to one decimal place.
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