Question

6. Explain how the parametric representations for x² + y2 = 4 differ. a) x = 2 cos(0), y = 2 sin(0) b) x = 2 sin(0), y = 2 cos(0) 7. Find dy for r = 3-2 sin(o) at the point o =. Leave your answer exact. dx

Answer 1

67 Here = 4 (1) as if 2005(C): Y = 25410) is the Parametric representation of c), Then if we choose 2 pornit (air) any 1 2 rolung Then the line Joining origin 0100) & (at) makes the angle d' with n-anis. if a= 2 Sin (0) 4 = 2 Cos (0) is the porta- metric representation of a), Then The line Joining origin 0100) & (art) makes the angle o with Joranis

Now, if s dr 3-2 sin o ) (1) - -2coso Now, a = coso S rl-sino) do dx= dnooso 2 ) t & Y= ssimo 3) de = dosing & rcoso do from 2 & 3) we get ay Smo dr + r caso do coso dr. - psino do smo ar a reaso coso an --psino do sino. (- 20050) & (3-2sind) caso COJO (-2005) (3-2 sito) sino Ľasing in 20] 4 sino corso + 3 euso dri da - 2005 0 – 3 sino + 2 sirene - 4 Sin (1) cws (24) + 3 cos (2) -2005 (9) - 35 + 2 sin - "4

-- x5+ 3rd + 2x2 -2X - 3x N - 2 ने 22 -3 ल 3 22 -3 3 4