Polar Coordinates (Edexcel A Level Further Maths: Core Pure): Exam Questions

(a) (i) Show on an Argand diagram the locus of points given by the values of  satisfying

Taking the initial line as the positive real axis with the pole at the origin and given that

      where 

(ii) show that this locus of points can be represented by the polar curve with equation

The set of points A is defined by

(b) (i) Show, by shading on your Argand diagram, the set of points .

(ii) Find the exact area of the region defined by , giving your answer in simplest form.

Figure 1 shows a sketch of two curves  and  with polar equations

The region  lies inside  and outside  and is shown shaded in Figure 1.

Show that the area of  is

where and  are integers to be determined.

Figure 1 shows the design for a table top in the shape of a rectangle . The length of the table, , is 1.2 m. The area inside the closed curve is made of glass and the surrounding area, shown shaded in Figure 1, is made of wood.

The perimeter of the glass is modelled by the curve with polar equation

where  is a constant.

a) Show that

Hence, given that  = 60 cm,

(b) find the area of the wooden part of the table top, giving your answer in m² to 3 significant figures.