Q. 6 Sketching parametric equations: ... [FREE SOLUTION]

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Chapter 9: Q. 6 (page 774)

Sketching parametric equations: Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.
$x = \tan t$ , $y = 1 + s e c^{2} t$ , $t 鈭� [- \frac{蟺}{2}, \frac{蟺}{2}]$ .

Short Answer

Expert verified

The curve is parabola and required graph is as follows,

Step by step solution

Step 1. Given Information.

The equations are $x = \tan t$ and $y = 1 + s e c^{2} t$ such that $t 鈭� [- \frac{蟺}{2}, \frac{蟺}{2}]$ .

Step 2. Explanation.

Start by eliminating the parameter. Square the equations for x and add 1..

$x^{2} + 1 = \tan^{2} t + 1$

Subtract 1 from y.

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

Apply trigonometric identity

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

Simplify the equation.

$y = x^{2} + 2$

The equation present parabola.

Step 3. Calculation.

Make a table to draw the table as follows,

t	$- \frac{蟺}{2}$	$- \frac{蟺}{4}$	0	$\frac{蟺}{4}$	$\frac{蟺}{2}$
$x = \tan t$	$鈭�$	-1	0	1	$鈭�$
$y = 1 + s e c^{2} t$	$鈭�$	3	2	3	$鈭�$

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.
$x = \tan t$ , $y = 1 + s e c^{2} t$ , $t 鈭� [- \frac{蟺}{2}, \frac{蟺}{2}]$ .

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=tant,y=1+sec2t,t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

Theoretical and Mathematical Physics

Discrete Mathematics

Logic and Functions

Geometry

Mechanics Maths

Applied Mathematics

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.
$x = \tan t$ , $y = 1 + s e c^{2} t$ , $t 鈭� [- \frac{蟺}{2}, \frac{蟺}{2}]$ .