f=4 l=6

2) An illustrative figure for the limacon r = 2 + 4 sin 9 is shown below. //I I a \ + \.\ .i ' \ ll ' ' -5" \zas_s_y_s_M/' ' ' Consider the equation I" = f + (f + i) sin 3 for a limacon which will look similar. The set of questions below are based on the limacon equation 1" = f + (f +0511) 6, not the limacon illustrated above. (a) [5 pts] Find the polar coordinates of the entry and exit points for the inner loop (2 out of 5 pts). The angular coordinate should be in radian measure and in the interval [0, 27:]. Also find the slopes of tangents and equations of tangents at the entry and exit points of the inner loop. (b) [5 pts] Find the area bounded by the limacon in the first quadrant that is outside the inner loop and inside the outer loop. (c) [5 pts] Find the length of complete inner loop. Use trapezoidal rule with four subintervals of equal length