Chapter 9: Q 51. (page 731)

In Exercises 48–55 convert the equations given in rectangular coordinates to equations in polar coordinates.
$y = x$

Short Answer

Expert verified

The required equation is $θ = \frac{π}{4}$ .

Step by step solution

Step 1. Given information.

The given equation in rectangular coordinates is:

$y = x$

Step 2. Find the equation in rectangular coordinates.

$y = x$

As we know that in polar coordinates $x = r \cos θ and y = r \sin θ$ , then substitute the value of yand x,

$r \cos θ = r \sin θ$

Divide both sides by r,

$\frac{r \cos θ}{r} = \frac{r \sin θ}{r} \cos θ = \sin θ$

Divide both sides by localid="1649348673648" $\sin θ$ ,

$\frac{\cos θ}{\sin θ} = \frac{\sin θ}{\sin θ} \cot θ = 1 θ = \frac{π}{4} [\cot \frac{π}{4} = 1]$

Therefore, the equation in polar coordinates islocalid="1649348683160" $θ = \frac{π}{4}$ .

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In Exercises 48–55 convert the equations given in rectangular coordinates to equations in polar coordinates.
$y = x$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the equation in rectangular coordinates.

One App. One Place for Learning.

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In Exercises 48–55 convert the equations given in rectangular coordinates to equations in polar coordinates.y=x

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the equation in rectangular coordinates.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Pure Maths

Probability and Statistics

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Exercises 48–55 convert the equations given in rectangular coordinates to equations in polar coordinates.
$y = x$