Q28E Give an example of a parametriza... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 3: Q28E (page 120)

Give an example of a parametrization of the ellipse
$x^{2} + \frac{y^{2}}{4} = 1$
in ${鈩�}^{2}$ . See Example .

Short Answer

Expert verified

$[\begin{matrix} \cos (t) \\ 2 \sin (t) \end{matrix}]$ is a parametrization of the ellipse $x^{2} + \frac{y^{2}}{4} = 1$ in ${鈩�}^{2}$ .

Step by step solution

Consider the parameters.

The image of a function consists of all the values the function takes in its target space. If f is a function from X to Y, then

$i m a g e (f) = \{f (x : x i n X)\} = \{b i n Y : b = f (x), f o r s o m e x i n X\}$

The standard form of an ellipse is, $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$

The parametrization of this ellipse is,

$x = (a) \cos (t), y = (b) \sin (t) [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} (a) \cos (t) \\ (b) \sin (t) \end{matrix}]$

The ellipse equation is, $\frac{x^{2}}{1} + \frac{y^{2}}{4} = 1$

The parametrization of this ellipse is,

$x = (1) \cos (t), Y = (2) \sin (t) [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} (1) \cos (t) \\ (2) \sin (t) \end{matrix}]$

Final answer.

$[\begin{matrix} \cos (t) \\ 2 \sin (t) \end{matrix}]$ is a parametrization of the ellipse $x^{2} + \frac{y^{2}}{4} = 1$ in ${鈩�}^{2}$ .

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91影视

Give an example of a parametrization of the ellipse
$x^{2} + \frac{y^{2}}{4} = 1$
in ${鈩�}^{2}$ . See Example .

Short Answer

Step by step solution

Consider the parameters.

Final answer.

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91影视

Give an example of a parametrization of the ellipse x2+y24=1in鈩�2 . See Example .

Short Answer

Step by step solution

Consider the parameters.

Final answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Probability and Statistics

Decision Maths

Theoretical and Mathematical Physics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Give an example of a parametrization of the ellipse
$x^{2} + \frac{y^{2}}{4} = 1$
in ${鈩�}^{2}$ . See Example .