Chapter 9: Q. 58 (page 568)

In Problems55–66, the rectangular coordinates of a point are given. Find polar coordinates for each point.
$(0, - 2)$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given Information

We are given rectangular coordinates of a point,

$(0, - 2)$

We have to find polar coordinates of given point.

Step 2. Finding the polar coordinates

The point $(0, - 2)$ lies in the third quadrant, so

$x = r \cos θ r \cos θ = 0 - (1) y = r \sin θ r \sin θ = - 2 - (2)$

Squaring both side and adding the two equations, we get

$(r \cos θ)^{2} + (r \sin θ)^{2} = 0^{2} + (- 2)^{2} r^{2} (\cos^{2} θ + \sin^{2} θ) = 4 r^{2} = 4 r = 2$

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

role="math" localid="1646730385944" $θ = \tan^{- 1} \frac{- 2}{0} θ = \tan^{- 1} - \infty θ = - \frac{π}{2}$

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

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In Problems55–66, the rectangular coordinates of a point are given. Find polar coordinates for each point.
$(0, - 2)$

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,-2

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

Calculus

Statistics

Mechanics Maths

Geometry

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems55–66, the rectangular coordinates of a point are given. Find polar coordinates for each point.
$(0, - 2)$