Chapter 9: Q. 10. (page 755)

Explain how to use parametric equations to transform a
polar function $r = f (θ)$

Short Answer

Expert verified

The parametric equations are $x = (1 - \sin θ) \cos θ, y = (1 - \sin θ) \sin θ$

Step by step solution

Given information

The polar function is $r = f (θ)$

The objective is to transform the polar equation of the form r=f(θ) into the parametric equations.

The function $r = f (θ)$ is simply expressed using parametric equations of the form $x = x (θ), y = y (θ)$ where $θ$ is the parameter.

To convert polar coordinates into rectangle coordinates $x = r \cos θ, y = r \sin θ$

write the parametric equations for r=1-sinθ

If $r = f (θ)$ then,

$x = f (θ) \cos θ, y = f (θ) \sin θ .$

The parametric equations for $r = 1 - \sin θ$

The parametric equations have the following form:

$x = f (θ) \cos θ, y = f (θ) \sin θ$

Then the parametric equations are:

$x = (1 - \sin θ) \cos θ, y = (1 - \sin θ) \sin θ$

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Explain how to use parametric equations to transform a
polar function $r = f (θ)$

Short Answer

Step by step solution

Given information

The objective is to transform the polar equation of the form r=f(θ) into the parametric equations.

write the parametric equations for r=1-sinθ

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Explain how to use parametric equations to transform apolar function r=f(θ)

Short Answer

Step by step solution

Given information

The objective is to transform the polar equation of the form r=f(θ) into the parametric equations.

write the parametric equations for r=1-sinθ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Applied Mathematics

Geometry

Mechanics Maths

Statistics

Study anywhere. Anytime. Across all devices.

Explain how to use parametric equations to transform a
polar function $r = f (θ)$