Challenging +1.8 This is a multi-part Further Maths polar coordinates question requiring sketching a rose curve, computing an area integral, and finding tangents parallel to the initial line using dy/dx = 0. The tangent condition requires implicit differentiation and solving transcendental equations, which is conceptually demanding and goes beyond routine FP2 exercises.
5. (a) Sketch the curve with polar equation \(\quad r = 3 \cos 2 \theta , \quad - \frac { \pi } { 4 } \leq \theta < \frac { \pi } { 4 }\)
(b) Find the area of the smaller finite region enclosed between the curve and the half-line
$$\theta = \frac { \pi } { 6 }$$
(c) Find the exact distance between the two tangents which are parallel to the initial line.
(8)(Total 16 marks)
5. (a) Sketch the curve with polar equation $\quad r = 3 \cos 2 \theta , \quad - \frac { \pi } { 4 } \leq \theta < \frac { \pi } { 4 }$\\
(b) Find the area of the smaller finite region enclosed between the curve and the half-line
$$\theta = \frac { \pi } { 6 }$$
(c) Find the exact distance between the two tangents which are parallel to the initial line.\\
(8)(Total 16 marks)\\
\hfill \mbox{\textit{Edexcel FP2 2004 Q5 [16]}}