Chapter 9: Q 6 (page 721)

Use the results of Exercise $3$ 3 to analyze the direction of
motion for the parametric curves given by the equations in
Exercises $5 - 8$
$x = \sin t, y = \cos t, t \in ℝ$

Short Answer

Expert verified

The required answer is the direction of motion is clockwise.

Step by step solution

Given information

The parametric equations :

$x = \sin t, y = \cos t, t \in ℝ$

Find the parametric equations that move in different directions.

The function $x = \sin t$

Differentiate in terms of $t$

$x^{1} (t) = \frac{d}{d t} (\sin t) x^{1} (t) = \cos t x^{1} (t) > 0$

The function $y = \cos t$

Differentiate in terms of $t$

$y^{'} (t) = \frac{d}{d t} (\cos t) y^{1} (t) = - \sin t < 0$

That $x^{1} (t) > 0 a n d y (t) < 0$

Find the direction of motion for the parametric curves given by the equations

When $t = 0$

$(x, y) = (\sin t, \cos t) (x, y) = (\sin 0, \cos 0) (x, y) = (0, 0)$

The value of $x$ increases as $t$ increases while the value of $y$ decreases

Therefore the direction of motion is clockwise.

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Use the results of Exercise $3$ 3 to analyze the direction of
motion for the parametric curves given by the equations in
Exercises $5 - 8$
$x = \sin t, y = \cos t, t \in ℝ$

Short Answer

Step by step solution

Given information

Find the parametric equations that move in different directions.

Find the direction of motion for the parametric curves given by the equations

One App. One Place for Learning.

Most popular questions from this chapter

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Use the results of Exercise 33 to analyze the direction ofmotion for the parametric curves given by the equations inExercises 5-8x=sint,y=cost,t∈ℝ

Short Answer

Step by step solution

Given information

Find the parametric equations that move in different directions.

Find the direction of motion for the parametric curves given by the equations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Applied Mathematics

Decision Maths

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Use the results of Exercise $3$ 3 to analyze the direction of
motion for the parametric curves given by the equations in
Exercises $5 - 8$
$x = \sin t, y = \cos t, t \in ℝ$