Question

Homework #6.3, Math 111, Due Friday, November 22. Complete the problems on a separate sheet of paper. Answer in complete sentences, and show your work when necessary. Make a copy for your notes. 9.3 Polar Coordinates There is a very specific set of parametric curves that is worth diving into: polar coordinates. Basically it makes circular things easier to formulate. 1. Write the two sets of equations for converting Cartesian to polar and vice versa. 1. I= y= 2. p2 = tan = 2. Convert the polar coordinates to Cartesian coordinates: (1, -37/4) and (2, -27/3). 3. Convert the Cartesian coordinates to polar coordinates (with r > 0): (1.1) and (-1,2). 4. Sketch the curve r = 2 sin ở by using a table (follow Example 6). 5. Sketch the curve r = 1 + cose by using a table (follow Example 7).

Answer 1

U-1 na escase 7 (ii) y = r sind iii) x (asot Sired) = x +42 Now As casot sented = 1, so, we get, in) = r + 48 7 r sind r card (1) tuno= ut Griven, r =1, 0= -3 11 Sol X=l.cos(-); y = 1. sein (-2) * = aru ; yo - Sinza * ; 4=

N = cas (es) ; ya d sin (-25) x= a cos (45) ; y = - 2 Seinle T) m=cos (3+)y- 2 sin (5+) x = - 2 sin I ; Y = -2 cost *Ende ; 4= -2se x=-1 y = - 13 0-3 §) *I, 9-1 Then, r = (14.ga) - 1+1=2 r= I2 . As ro r=12

Alid, tand = 7 = 7 = 1 > tunda > 0 (1,1) -> (Je, ) real, y = 2 r = x² + y2 = 1+4= 5 as r so, so pr=05/ Also 9 tund = 1 tond = -2 t = tant (-2) 0 = - tant (2) ba Hence, Honey (+1, 2) (so, -trile))

Q-u r= 2 sind we can see Art d=0 as r=o At d I s r= l sa = d = 317 » r=-2 d=25 as r=0 Thus, a= 2 serio Represent The circle of Radius "2" For ordea T er = 1+ losd At 5 lola d=o os r=2 o = 7 s er=1 d = IT a rao d=217 sr=2 This Again Represent a circ of Radius "g