Q 29. In Exercises 24鈥�31 find all po... [FREE SOLUTION]

Chapter 9: Q 29. (page 730)

In Exercises 24鈥�31 find all polar coordinate representations for the point given in rectangular coordinates.
$(6, 2 \sqrt{3})$

Short Answer

Expert verified

The polar coordinates are $(4 \sqrt{3}, \frac{蟺}{6} + 2 办蟺) and (- 4 \sqrt{3}, \frac{7 蟺}{6} + 2 办蟺)$ , for any integer k.

Step by step solution

Step 1. Given information.

The given rectangular coordinate is:

$(6, 2 \sqrt{3})$

Here $x = 6 and y = 2 \sqrt{3}$ .

Step 2. Find the value of r.

To find the value of r, use the formula $r = \sqrt{x^{2} + y^{2}}$ :

$r = \sqrt{{(6)}^{2} + {(2 \sqrt{3})}^{2}} r = \sqrt{36 + 12} r = \sqrt{48} r = 卤 4 \sqrt{3}$

Step 3. Find the value of θ.

Use the formula $\tan 胃 = \frac{y}{x}$ ,

$\tan 胃 = \frac{y}{x}; then 胃 = \tan^{- 1} (\frac{y}{x}) 胃 = \tan^{- 1} (\frac{2 \sqrt{3}}{6}) 胃 = \tan^{- 1} (\frac{\sqrt{3}}{3}); 胃 = \tan^{- 1} (\frac{\sqrt{3}}{\sqrt{3} 路 \sqrt{3}}) 胃 = \tan^{- 1} (\frac{1}{\sqrt{3}}) 胃 = \frac{蟺}{6}, \frac{7 蟺}{6}$

Step 4. Find the polar coordinates.

Take $r = 4 \sqrt{3}, 胃 = \frac{蟺}{6}; then (r, 胃) = (4 \sqrt{3}, \frac{蟺}{6})$ ,

The coordinates of $(r, 胃) are (4 \sqrt{3}, \frac{蟺}{6} + 2 办蟺)$ , for any integer k.

Now take $r = - 4 \sqrt{3}, 胃 = \frac{7 蟺}{6}; then (r, 胃) = (- 4 \sqrt{3}, \frac{7 蟺}{6})$ ,

The coordinates of $(r, 胃) are (- 4 \sqrt{3}, \frac{7 蟺}{6} + 2 办蟺)$ , for any integer k.

Therefore, all the polar coordinates are $(4 \sqrt{3}, \frac{蟺}{6} + 2 办蟺) and (- 4 \sqrt{3}, \frac{7 蟺}{6} + 2 办蟺)$ , for any integer k.

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91影视

In Exercises 24鈥�31 find all polar coordinate representations for the point given in rectangular coordinates.
$(6, 2 \sqrt{3})$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the value of r.

Step 3. Find the value of θ.

Step 4. Find the polar coordinates.

One App. One Place for Learning.

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91影视

In Exercises 24鈥�31 find all polar coordinate representations for the point given in rectangular coordinates.6,23

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the value of r.

Step 3. Find the value of θ.

Step 4. Find the polar coordinates.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Logic and Functions

Pure Maths

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

In Exercises 24鈥�31 find all polar coordinate representations for the point given in rectangular coordinates.
$(6, 2 \sqrt{3})$