Chapter 9: Q. 4 (page 774)

Sketching parametric equations: Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.
$x = \sin t$ , $y = \cos^{2} t$ , $t \in [0, 4 π]$ .

Short Answer

Expert verified

The graph is parabola.

Step by step solution

Step 1. Given Information.

The equation are $x = \sin t$ and $y = \cos^{2} t$ such that $t \in [0, 4 π]$

Step 2. Explanation.

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

$x^{2} = \sin^{2} t$

Apply the Pythagorean identity.

$\sin^{2} t + \cos^{2} t = 1 x^{2} + y = 1$

Rewrite the equation.

role="math" localid="1652158119109" $y = - x^{2} + 1$

This is the equation of parabola.

Step 3. Calculation.

Make a table as follows,

t	0	$\frac{π}{2}$	$- \frac{π}{2}$	$4 π$
$x = \sin t$	$0$	1	-1	0
$y = \cos^{2} t$	1	0	0	1

Step 4. Draw the graph.

The required curve is as follows,

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Sketching parametric equations: Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.
$x = \sin t$ , $y = \cos^{2} t$ , $t \in [0, 4 π]$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Calculation.

Step 4. Draw the graph.

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Sketching parametric equations: Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.x=sint,y=cos2t,t∈0,4π.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Calculation.

Step 4. Draw the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Geometry

Calculus

Applied Mathematics

Probability and Statistics

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.
$x = \sin t$ , $y = \cos^{2} t$ , $t \in [0, 4 π]$ .