Chapter 9: Q. 64 (page 568)

In Problems55–66, the rectangular coordinates of a point are given. Find polar coordinates for each point.
$(- 0.8, - 2.1)$

Short Answer

Expert verified

The polar coordinates is $(\sqrt{5.05}, 4.34)$ .

Step by step solution

Step 1. Given Information

We are given rectangular coordinates of a point,

$(- 0.8, - 2.1)$

We have to find polar coordinates of given point.

Step 2. Finding the polar coordinates

The distance of the point $(- 0.8, - 2.1)$ from origin is given by,

$r = \sqrt{x^{2} + y^{2}} r = \sqrt{{(- 0.8)}^{2} + {(- 2.1)}^{2}} = \sqrt{0.64 + 4.41} = \sqrt{5.05}$

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

localid="1646797452204" $θ = \tan^{- 1} (\frac{- 2.1}{- 0.8}) = \tan^{- 1} (2.625) = - 1.2$

Since, the point is in the third quadrant, so by adding $π = 3.14$ , we get the angle in third quadrant.

$θ = 3.14 + 1.2 θ = 4.34$

So, the polar coordinate will be role="math" localid="1646797577326" $(\sqrt{5.05}, 4.34)$ .

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In Problems55–66, the rectangular coordinates of a point are given. Find polar coordinates for each point.
$(- 0.8, - 2.1)$

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. -0.8,-2.1

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

Discrete Mathematics

Decision Maths

Mechanics Maths

Probability and Statistics

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

In Problems55–66, the rectangular coordinates of a point are given. Find polar coordinates for each point.
$(- 0.8, - 2.1)$