Chapter 9: Q. 59 (page 568)

In Problems55–66, the rectangular coordinates of a point are given. Find polar coordinates for each point.
$(1, - 1)$

Short Answer

Expert verified

The polar coordinates is $(\sqrt{2}, - \frac{π}{4})$ .

Step by step solution

Step 1. Given Information

We are given rectangular coordinates of a point,

$(1, - 1)$

We have to find polar coordinates of given point.

Step 2. Finding the polar coordinates

The distance of the point $(1, - 1)$ from origin is given by,

$r = \sqrt{x^{2} + y^{2}} r = \sqrt{1^{2} + (- 1)^{2}} = \sqrt{1 + 1} = \sqrt{2}$

Step 3. Finding the polar coordinates

We know that,

$\tan θ = \frac{y}{x}, so θ = \tan^{- 1} \frac{y}{x}, - \frac{π}{2} < θ < \frac{π}{2}$

Putting values, we get

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

So, the polar coordinate will be $(\sqrt{2}, - \frac{π}{4})$ .

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In Problems55–66, the rectangular coordinates of a point are given. Find polar coordinates for each point.
$(1, - 1)$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the polar coordinates

Step 3. Finding the polar coordinates

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In Problems55–66, the rectangular coordinates of a point are given. Find polar coordinates for each point.1,-1

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the polar coordinates

Step 3. Finding the polar coordinates

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Mechanics Maths

Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problems55–66, the rectangular coordinates of a point are given. Find polar coordinates for each point.
$(1, - 1)$