Question

Select the first set of parametric equations, x = a cos(bt), y = c sin(dt). (a) Set the equations to x = 2 cos(t), y = 2 sin(t) using the sliders for a, b, c, and d. Describe the parametric curve. This answer has not been graded yet. What minimum parameter domain is required to draw the entire circle? Osts How many times is the circle traced out for Osts 4?

Answer 1

Solution :- 2 = 2 cost , y = 2 sint. aj The curve is a circle of radius 2. Haversed anticlockwise , ast increases. Minimum parametric domain required to draw the entire circle ost can I y I=0) or (+=277) (t = 1) x²+y2=4 or r= 2cost y = 2sint For Olt (45) circle traversed 2 times. -

b) لما 2cos (2+) Now radius is same as part a)(ie, 2 y = 2 sin 12t) but radius is traversed 2 times fast ost L40| circle traversed 4 times OL Ł CT circle traversed anticlockwise, i time completely t increases as c) x = 2 cos (-2t) Radius and circle remain same as y = 2 = 2 sin (-20 in part but Now it is traversed in clockwise mannen part b) Radius 3 center origin, travel once in clockwise direction Ozt<411 -C=3 as radius 3. as a cos (67) y = c sin(dt) b=d = -1/2 (for clockwise traversing, -re sign) =(x,y) 9 - (3cos($) 3 sin())