Chapter 9: Q. 4 (page 631)

Convert $(2, 2 \sqrt{3})$ from rectangular coordinates to polar coordinates $(r, θ)$ , where $r > 0$ and $0 \leq θ < 2 π$ .

Short Answer

Expert verified

The polar point is $(4, \frac{π}{3})$ .

Step by step solution

Step 1. Given information

We are given a point $(2, 2 \sqrt{3})$ .

We have to convert the given point from rectangular coordinates to polar coordinates.

Step 2. Converting the point

We know that,

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

So, putting values, we get

$r^{2} = 2^{2} + (2 \sqrt{3})^{2} r = \sqrt{4 + 12} r = \sqrt{16} r = 4$

Step 3. Converting the point

Also, we know that

$\tan θ = \frac{y}{x}$

so, putting values, we get

$\tan θ = \frac{2 \sqrt{3}}{2} θ = \tan^{- 1} \sqrt{3} θ = \frac{π}{3}$

Hence, the polar point is role="math" localid="1647002989966" $(4, \frac{π}{3})$ .

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Convert $(2, 2 \sqrt{3})$ from rectangular coordinates to polar coordinates $(r, θ)$ , where $r > 0$ and $0 \leq θ < 2 π$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Converting the point

Step 3. Converting the point

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Convert $(2, 2 \sqrt{3})$ from rectangular coordinates to polar coordinates $(r, θ)$ , where $r > 0$ and $0 \leq θ < 2 π$ .