Chapter 9: Q. 14 (page 730)

Find all polar coordinates that represent the point $(0, 1)$ given in rectangular coordinates.

Short Answer

Expert verified

The polar coordinates that represent the point $(0, 1)$ are $(- 1, - \frac{π}{2} + 2 k π)$ and $(1, \frac{π}{2} + 2 k π)$ , for any integer K.

Step by step solution

Given information

The rectangular coordinate $(0, 1)$

Calculation

Consider the rectangular coordinate $(0, 1)$ .

The objective is to convert the rectangular coordinates to polar coordinates.

In the coordinate $(0, 1), x = 0$ and $Y = 1$ .

To find the value of $r$ use the equation $r = \sqrt{x^{2} + y^{2}}$ .

Then, $r = \sqrt{x^{2} + y^{2}}$

$r = \sqrt{x^{2} + y^{2}}$

$r = \sqrt{(0)^{2} + (1)^{2}}$ [since $x = 0, y = 1]$

$r = \pm 1$

By substituting $x, y$ in the formula,

$θ = \tan^{- 1} (\frac{1}{0})$ [since $x = 0, y = 1]$

$θ = \tan^{- 1} (\infty)$

$θ - \frac{π}{2}, \frac{π}{2}, \frac{3 π}{2} [since \tan \frac{π}{2} = \tan \frac{3 π}{2} = \infty]$

Take $r = - 1, θ = - \frac{π}{2}$ .

Then $(r, θ) = (- 1, - \frac{π}{2})$

Thus, the coordinates of $(r, θ)$ are $(- 1, - \frac{π}{2} + 2 k π)$ , for any integer $k$ .

Now take $r = 1, θ = \frac{π}{2}$ .

$(r, θ) = (1, \frac{π}{2})$

The coordinates of $(r, θ)$ are $(1, \frac{π}{2} + 2 k π)$ , for any integer $k$ . Therefore, the polar coordinates are $(- 1, - \frac{π}{2} + 2 k π)$ and $(1, \frac{π}{2} + 2 k π)$ , for any integer $k$ .

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Find all polar coordinates that represent the point $(0, 1)$ given in rectangular coordinates.

Short Answer

Step by step solution

Given information

Calculation

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Find all polar coordinates that represent the point (0,1)given in rectangular coordinates.

Short Answer

Step by step solution

Given information

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Decision Maths

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Study anywhere. Anytime. Across all devices.

Find all polar coordinates that represent the point $(0, 1)$ given in rectangular coordinates.