Q. 5 Sketching parametric equations: ... [FREE SOLUTION]

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Chapter 9: Q. 5 (page 774)

Sketching parametric equations: Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.
$x = s e c t$ , $y = \tan t$ $t 鈭� [- \frac{蟺}{2}, \frac{蟺}{2}]$ .

Short Answer

Expert verified

The curve is hyperbola and graph is as follows,

Step by step solution

Step 1. Given Information.

The equations are $x = s e c t$ and $y = \tan t$ such as $t 鈭� [- \frac{蟺}{2}, \frac{蟺}{2}]$ .

Step 2. Explanation.

Start by eliminating the parameter. Square the equations for x and y.

$x^{2} = s e c^{2} t$

$y^{2} = \tan^{2} t$

Apply the Pythagorean identity.

$s e c^{2} t - \tan^{2} t = 1 x^{2} - y^{2} = 1$

The equation represents hyperbola.

Step 3. Calculation.

Make a table to draw the curve.

t	$- \frac{蟺}{2}$	$- \frac{蟺}{4}$	0	$\frac{蟺}{4}$	$\frac{蟺}{2}$
$x = s e c t$	$鈭�$	$\sqrt{2}$	1	$\sqrt{2}$	$鈭�$
$y = \tan t$	0	-1	0	1	0

Step 4. Graph.

The required graph is as follows,

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91影视

Sketching parametric equations: Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.
$x = s e c t$ , $y = \tan t$ $t 鈭� [- \frac{蟺}{2}, \frac{蟺}{2}]$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Calculation.

Step 4. Graph.

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91影视

Sketching parametric equations: Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.x=sect,y=tantt鈭�-蟺2,蟺2.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Calculation.

Step 4. Graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Pure Maths

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

Sketching parametric equations: Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.
$x = s e c t$ , $y = \tan t$ $t 鈭� [- \frac{蟺}{2}, \frac{蟺}{2}]$ .