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....
just make circle questions which 2,(b) and 3,(i) thank you 2. (Polar Coordinates: Polar Plots). (a) Consider the curve given in polar coordinates (i) Use a scientific calculator to fill in the following table with the (approximations of) values of the function r(0) on π, π r(e) (the approximations of the values r(e) must be good to at least two decimal places). (i) Use the graph paper for the polar coordinate system (attached to the assignment sheet) to plot the...
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 points of intersection. Also indicate the values of theta that eive complete cycle for each curve. a b. Discuss the symmetry of each curve. ulate the area for the region of overlap that you shaded and described in part a. Show all steps...
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...
(a) Label each of the polar equations with the corresponding graphs labeled I-III, or mark None' if the graph of the equation is not shown. Justify your answers. 1. r = 62, 0 <O< 167 2. r= 2+ sin(30) 3. r = 2 cos(0) 4. r= 1 + 2 cos(0) I II III pilot (b) Set up (but do not compute) the integral to determine the area of the shaded region bounded by the curve in polar coordinates. X r...
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.
d) Find the area between the two curves (the shaded region). 2 + (2 r=2+cos 2θ ra sin 2θ d) Find the area between the two curves (the shaded region). 2 + (2 r=2+cos 2θ ra sin 2θ
2) Consider polar curre r=4coso and r=1+2 caso r=1+2 cos r=4coso B A a) Find ALL intersection points of the two curves, where osos2a, and Express them in polar coordinates b) Find the area inside the shaded loop of the curve r=1+2 cose C) Find the length of r=4cose from A to B as a increases, where A is the intersection of the two curres in quadrant II, and B is the intersection of the curve r=4cose with the positive...
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...
Below is a graph of the circle r = 4 cos θ and the circle r = 2. y x −1 1 −2 2 −2 −1 1 2 3 4 (i) Find the polar coordinates of both intersection points of these two curves. (Note: show all of your work) (ii) Set up (but do not evaluate) an integral that represents the area inside of the circle r = 4 cos(θ) and outside of the circle r = 2. (Note: no...