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 $t \in [0, 2 π]$ .

Short Answer

Expert verified

The required parametric equations are $x = \sin t, y = \cos t$ .

Step by step solution

Given information

A curve starting at the point $(0, 1)$ with $t \in [0, 2 π]$ .

Calculation

Consider a curve starting at the point $(0, 1)$ with $t \in [0, 2 π]$ .

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

$(x, y) = (r \sin t, r \cos t)$

Here $r = 1$ then,

$(x, y) = (1 \cdot \sin t, 1 \cdot \cos t) (x, y) = (\sin t, \cos t)$

Thus,

$x = \sin t$ and 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 $x = \sin t, y = \cos t$ .

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The curve is a circle centered at the origin. It is traced once, clockwise, starting at the point $(0, 1)$ with $t \in [0, 2 π]$ .

Short Answer

Step by step solution

Given information

Calculation

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

Short Answer

Step by step solution

Given information

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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The curve is a circle centered at the origin. It is traced once, clockwise, starting at the point $(0, 1)$ with $t \in [0, 2 π]$ .