Question 11 The curve given by the polar equation Not yet answered T = a(1 cos 0) Marked out of 18 is called a The cardioid has equation P Flag question (2 + y? + az)? = a (z + y) %3D To sketch the graph of r = 4(1 cost) we first observe that if a point (r,e) lies on the graph then lies also on the same graph. This shows that the graph is symmetric about the Therefore, it suffices to let change between 0 and If e is then ris 0. Next, we compute the values of r for increasing values of e. If e is then r is approximately Similarly, if e is then r is Also if e is then r is approximately In the case of e=r/2 we have r=4 because is zero. If e is we have r is .Also, if e=5Tt/6 then r is approximately Finally, r is when e is Tt. em m 7m TE/6 8 T/4 1.17 2T/3 the line y=x+2 T/3 cosine 2 (r,-8) cardioid Cartesian 6. 7.46 y-axis 26 0.54 -is