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Chapter 9: Q. 36 (page 721)

The curve is a circle centered at the origin. It is traced once, clockwise, starting at the point (0,1) with t鈭�[0,2蟺].

Short Answer

Expert verified

The required parametric equations are x=sint,y=cost.

Step by step solution

01

Given information

A curve starting at the point (0,1)witht鈭�[0,2蟺].

02

Calculation

Consider a curve starting at the point (0,1)with t鈭�[0,2蟺].

The objective is to find the parametric equations which represent the given condition.

Given that the curve is centered at the origin ,traced once in clockwise direction.

The curve is a unit circle starting from the point (0,1)so the radius of the curve is 1 .

The parametric equations which move in a clockwise direction starting at (0,1)is given by

(x,y)=(rsint,rcost)

Herer=1then,

(x,y)=(1路sint,1路cost)(x,y)=(sint,cost)

Thus,

x=sintand forms a circle with center (0,0)and radius is Iwhich starts at (0,1)moving in clockvise direction.

Therefore, the required parametric equations are x=sint,y=cost.

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