Chapter 9: Q. 4 (page 629)

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

Short Answer

Expert verified

The polar co-ordinates are $(3 \sqrt{2}, 1.5574) a n d (- 3 \sqrt{2}, - 1.5574)$

Step by step solution

Step 1. Value of r

The co-ordinates are given as $(- 3, 3)$

We know, $r = \sqrt{x^{2} + y^{2}} r = \sqrt{3^{2} + {(- 3)}^{2}} r = 3 \sqrt{2}$

Step 2. Value of θ

The value of $θ$ can be found by,

$θ = \tan^{- 1} (y / x) = \tan^{- 1} (- 1 / 1) = 1.5574$

Step 3. Value of angle with negative r

When $r = - 3 \sqrt{2}$ , the ray will go in the opposite direction,

Therefore $θ = - 1.5574$

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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 $r > 0$ r 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. Value of angle with negative 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>0r 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. Value of angle with negative r

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Mechanics Maths

Decision Maths

Theoretical and Mathematical Physics

Calculus

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 $r > 0$ r and the other with $r < 0$ . Express $θ$ in radians