Q. 2 Examples: Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading. (a) Parametric equations with th... [FREE SOLUTION]

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Chapter 11
Q. 2 Examples: Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.

Chapter 11: Q. 2 Examples: Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading. (page 859)

(a) Parametric equations with three components for a
circular helix winding around the $x -$ axis

Short Answer

Expert verified

The image of the example has been added below.

Step by step solution

Step 1. Given Information

Parametric equations with three components for a

circular helix winding around the $x -$ axis.

Step 2. Taking example of circular helix

As the objective is to construct a parametric equation of circular helix winding at $x -$ axis

Taking example of circular helix

$r (t) = <t, t \cos t, t \sin t>, t 鈭� [0, 4 蟺]$

$x (t) = t . . . . . . (1)$

role="math" localid="1649625334832" $y (t) = t \cos t . . . . . . (2)$

$z (t) = t \sin t . . . . . . (3)$

Step 3. Tabulating different values of t

Making a table

$t$	$x (t) = t$	$y (t) = t \cos t$	$z (t) = t \sin t$	$(x, y, z)$
$0$	$0$	$5$	$0$	$(0, 0, 0)$
$蟺$	$蟺$	$- 蟺$	$0$	$(蟺, - 蟺, 0)$
$2 蟺$	$2 蟺$	$2 蟺$	$0$	$(2 蟺, 2 蟺, 0)$
$3 蟺$	$3 蟺$	$- 3 蟺$	$0$	$(3 蟺, 3 蟺, 0)$
$4 蟺$	$4 蟺$	$4 蟺$	$0$	$(4 蟺, 4 蟺, 0)$

Step 4. Making the helix

Image of the graph

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91影视

(a) Parametric equations with three components for a
circular helix winding around the $x -$ axis

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Taking example of circular helix

Step 3. Tabulating different values of t

Step 4. Making the helix

One App. One Place for Learning.

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91影视

(a) Parametric equations with three components for acircular helix winding around the x-axis

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Taking example of circular helix

Step 3. Tabulating different values of t

Step 4. Making the helix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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Probability and Statistics

Geometry

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

(a) Parametric equations with three components for a
circular helix winding around the $x -$ axis