1. The following questions involve the two polar curves: R 2+2sin20 and r 6sin 0 Sketch the curves and shade the region outside R and inside r. Use a large size graph paper and clearly indicate the p...
1. The following questions involve the two polar curves: R 2+2sin20 and r 6sin 6 Sketch the curves and shade the region outside R and inside r. Use a large size graph paper and clearly indicate the points of intersection. Also indicate the values of theta that give one complete cycle for each curve. Discuss the symmetry of each curve. a. b. Calculate the area for the region of overlap that you shaded and described in part a. Show all...
1 The following questions involve the two polar curves: Sketch the curves and shade the region outside R and inside r Use a large size graph paper a l clearly indicate the points of intersection. Also indicate the values of theta that give one complete cycle for each curve b. Discuss the symmetry of each curve c. Calculate th e area for the region of overlap that you shaded and described in part a. Show all steps clearly and neatly....
Let R be the region inside the graph of the polar curver=3 and outside the graph of the polar curve r=3(1 - cos 6). (a) Sketch the two polar curves in the xy-plane and shade the region R. (b) Find the area of R.
5. The graphs of the polar curves r-4 and r-3 + 2 cos θ are shown in the figure above. The curves intersect 3 (a) Let R be the shaded region that is inside the graph of r-4 and also outside the graph of r 34 2 cos θ, as shown in the figure above. Write an expression involving an integral for the area of R. (b) Find the slope of the line tangent to the graph of r :-3...
1. The polar curves r@) = 1 + 2 sin(39), r = 2, are graphed below. 2 (a) Find the area inside the larger loops and outside the smaller loops of the graph of r 12 sin(30). [Hint: Use symmetry, the answer is 3v3.] [Answer: sf-i.] quadrant where r is maximum? (b) Find the area outside the circle r 2 but inside the curve r 1+2 sin(30) (c) What is the tangent line to the curve r-1+2sin(30) at the point...