Question

Convert the rectangular coordinates to polar coordinates with

Answer 1

Given:

Rectangular coordinate = (8, 6)

To convert:

Rectangular coordinate to polar coordinate with r > 0 and 0 ≤ θ < 2π.

Solution:

Let us find r:

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

$r=\sqrt{8^{2}+6^{2}}$

$r=\sqrt{100}$

r = 10

Now, find θ:

$\tan \theta=\frac{y}{x}$

$\tan \theta=\frac{6}{8}$

Cancel the common factor 2.

$\tan \theta=\frac{3}{4}$

$\theta=\tan^{-1} \left(\frac{3}{4}\right)$

θ = 36.87°

The polar coordinates are (r, θ) = (10, 36.87°).