Q. 59 Convert the equations given in p... [FREE SOLUTION]

Chapter 9: Q. 59 (page 731)

Convert the equations given in polar coordinates to equations in rectangular coordinates
$胃 = \frac{k 蟺}{6}$ , for each positive integer k less than 12.

Short Answer

Expert verified

The equations in the polar for for different value of k:

x = \sqrt{3} y, k = 1 y = \sqrt{3} x, k = 2 x = 0, k = 3 y = - \sqrt{3} x, k = 4 x = - \sqrt{3} y, k = 5 y = 0, k = 6 x = \sqrt{3} y, k = 7 y = \sqrt{3} x, k = 8 x = 0, k = 9 y = - \sqrt{3} x, k = 10 x = - \sqrt{3} y, k = 11

Step by step solution

Step 1. Given information

$胃 = \frac{k 蟺}{6}$ ,for each positive integer k less than 12.

Step 2. Write equation in rectangular form for k=1

As we know that in polar form

胃 = \tan^{- 1} (\frac{y}{x})

So, when $k = 1$

role="math" localid="1652108770892" $胃 = \frac{蟺}{6} \tan^{- 1} (\frac{y}{x}) = \frac{蟺}{6} \frac{y}{x} = \tan (\frac{蟺}{6}) \frac{y}{x} = \frac{1}{\sqrt{3}} x = y \sqrt{3}$

Step 3. Write equation in the rectangular form for k=2

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

Step 4. Write equation in the rectangular form for k=3

$胃 = \frac{3 蟺}{6} 胃 = \frac{蟺}{2} \tan^{- 1} (\frac{y}{x}) = \frac{蟺}{2} \frac{y}{x} = \tan (\frac{蟺}{2}) \frac{y}{x} = \frac{1}{0} x = 0$

Step 5. Write equation in the rectangular form for k=4

$胃 = \frac{4 蟺}{6} 胃 = \frac{2 蟺}{3} \tan^{- 1} (\frac{y}{x}) = \frac{2 蟺}{3} \frac{y}{x} = \tan (\frac{2 蟺}{3}) \frac{y}{x} = - \sqrt{3} y = - x \sqrt{3}$

Step 6. Write equation in the rectangular form for k=5

$胃 = \frac{5 蟺}{6} \tan^{- 1} (\frac{y}{x}) = \frac{5 蟺}{6} \frac{y}{x} = \tan (\frac{5 蟺}{6}) \frac{y}{x} = - \frac{1}{\sqrt{3}} x = - y \sqrt{3}$

Step 7. Write equation in the rectangular form for k=6

$胃 = \frac{6 蟺}{6} 胃 = 蟺 \tan^{- 1} (\frac{y}{x}) = 蟺 \frac{y}{x} = 迟补苍蟺 \frac{y}{x} = 0 y = 0$

Step 8. Write equation in the rectangular form for k=7

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

Step 9. Write equation in the rectangular form for k=8

$胃 = \frac{8 蟺}{6} 胃 = \frac{4 蟺}{3} \tan^{- 1} (\frac{y}{x}) = \frac{4 蟺}{3} \frac{y}{x} = \tan (\frac{4 蟺}{3}) \frac{y}{x} = \sqrt{3} y = x \sqrt{3}$

Step 10. Write equation in the rectangular form for k=9

$胃 = \frac{9 蟺}{6} 胃 = \frac{3 蟺}{2} \tan^{- 1} (\frac{y}{x}) = \frac{3 蟺}{2} \frac{y}{x} = \tan (\frac{3 蟺}{2}) \frac{y}{x} = \frac{1}{0} x = 0$

Step 11. Write equation in the rectangular form for k=10

$胃 = \frac{10 蟺}{6} 胃 = \frac{5 蟺}{3} \tan^{- 1} (\frac{y}{x}) = \frac{5 蟺}{3} \frac{y}{x} = \tan (\frac{5 蟺}{3}) \frac{y}{x} = - \sqrt{3} y = - x \sqrt{3}$

Step 12. Write equation in the rectangular form for k=11

$胃 = \frac{11 蟺}{6} \tan^{- 1} (\frac{y}{x}) = \frac{11 蟺}{6} \frac{y}{x} = \tan (\frac{11 蟺}{6}) \frac{y}{x} = - \frac{1}{\sqrt{3}} x = - y \sqrt{3}$

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91影视

Convert the equations given in polar coordinates to equations in rectangular coordinates
$胃 = \frac{k 蟺}{6}$ , for each positive integer k less than 12.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write equation in rectangular form for k=1

Step 3. Write equation in the rectangular form for k=2

Step 4. Write equation in the rectangular form for k=3

Step 5. Write equation in the rectangular form for k=4

Step 6. Write equation in the rectangular form for k=5

Step 7. Write equation in the rectangular form for k=6

Step 8. Write equation in the rectangular form for k=7

Step 9. Write equation in the rectangular form for k=8

Step 10. Write equation in the rectangular form for k=9

Step 11. Write equation in the rectangular form for k=10

Step 12. Write equation in the rectangular form for k=11

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91影视

Convert the equations given in polar coordinates to equations in rectangular coordinates 胃=k蟺6, for each positive integer k less than 12.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write equation in rectangular form for k=1

Step 3. Write equation in the rectangular form for k=2

Step 4. Write equation in the rectangular form for k=3

Step 5. Write equation in the rectangular form for k=4

Step 6. Write equation in the rectangular form for k=5

Step 7. Write equation in the rectangular form for k=6

Step 8. Write equation in the rectangular form for k=7

Step 9. Write equation in the rectangular form for k=8

Step 10. Write equation in the rectangular form for k=9

Step 11. Write equation in the rectangular form for k=10

Step 12. Write equation in the rectangular form for k=11

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Decision Maths

Theoretical and Mathematical Physics

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Convert the equations given in polar coordinates to equations in rectangular coordinates
$胃 = \frac{k 蟺}{6}$ , for each positive integer k less than 12.