Chapter 9: Q. 6 (page 629)

The rectangular coordinates of a point are given. Find two pairs of polar coordinates $(r, θ)$ for each point, one with $r > 0$ and the other with $r < 0$ Express $θ$ in radians .

Short Answer

Expert verified

The polar co-ordinates are $(5, 0.93)$ and $(- 5, 4.07)$

Step by step solution

Step 1. Value of r

The given rectangular co-ordinate is $(3, 4)$

We know,

$r = \sqrt{x^{2} + y^{2}} r = \sqrt{3^{2} + 4^{2}} = \sqrt{9 + 16} = \sqrt{25} = 5$

Step 2. Value of θ

Now, the angle $θ$ can be found by

$θ = \tan^{- 1} (\frac{y}{x}) θ = \tan^{- 1} (\frac{4}{3}) = \tan^{- 1} (1.33) = 0.93$

So the point becomes, $(5, 0.93)$

Step 3. Polar co-ordinate with negative value of r

Now,

when $r = - 5$ $r = - 5$

The ray will go in the opposite direction,

$θ = \tan^{- 1} (\frac{y}{x}), - \frac{π}{2} < θ < \frac{π}{2} θ = \tan^{- 1} (\frac{4}{3}) = \tan^{- 1} (1.33) = - 4.07$

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The rectangular coordinates of a point are given. Find two pairs of polar coordinates $(r, θ)$ for each point, one with $r > 0$ and the other with $r < 0$ Express $θ$ in radians .

Short Answer

Step by step solution

Step 1. Value of r

Step 2. Value of θ

Step 3. Polar co-ordinate with negative value of r

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The rectangular coordinates of a point are given. Find two pairs of polar coordinates (r,θ)for each point, one with r>0and the other with r<0 Express θ in radians .

Short Answer

Step by step solution

Step 1. Value of r

Step 2. Value of θ

Step 3. Polar co-ordinate with negative value of r

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Probability and Statistics

Theoretical and Mathematical Physics

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

The rectangular coordinates of a point are given. Find two pairs of polar coordinates $(r, θ)$ for each point, one with $r > 0$ and the other with $r < 0$ Express $θ$ in radians .