Chapter 9: Q. 58 (page 731)

convert the equations given in polar coordinates to equations in rectangular coordinates
$θ = 0, θ = \frac{π}{4}, θ = - \frac{π}{2}$

Short Answer

Expert verified

The equations in rectangular form are:

$y = 0 y = x x = 0$

Step by step solution

Step 1. Given information

Equation in polar form

θ = 0, θ = \frac{π}{4}, θ = - \frac{π}{2}

Step 2. Convert the equations in rectangular form.

As we know that in polar form

$θ = \tan^{- 1} (\frac{y}{x})$

So,

localid="1652107972021" $θ = 0 \tan^{- 1} (\frac{y}{x}) = 0 \frac{y}{x} = \tan 0 \frac{y}{x} = 0 y = 0$

$θ = \frac{π}{4} \tan^{- 1} (\frac{y}{x}) = \frac{π}{4} \frac{y}{x} = \tan \frac{π}{4} \frac{y}{x} = 1 y = x$

$θ = - \frac{π}{2} \tan^{- 1} (\frac{y}{x}) = - \frac{π}{2} \frac{y}{x} = \tan (- \frac{π}{2}) \frac{y}{x} = - \frac{1}{0} x = 0$

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convert the equations given in polar coordinates to equations in rectangular coordinates
$θ = 0, θ = \frac{π}{4}, θ = - \frac{π}{2}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Convert the equations in rectangular form.

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convert the equations given in polar coordinates to equations in rectangular coordinatesθ=0,θ=π4,θ=-π2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Convert the equations in rectangular form.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Logic and Functions

Applied Mathematics

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

convert the equations given in polar coordinates to equations in rectangular coordinates
$θ = 0, θ = \frac{π}{4}, θ = - \frac{π}{2}$