Given:
Rectangular coordinate = (8, 6)
To convert:
Rectangular coordinate to polar coordinate with r > 0 and 0 ≤ θ < 2π.
Solution:
Let us find r:
[tex]r=\sqrt{x^{2}+y^{2}}[/tex]
[tex]r=\sqrt{8^{2}+6^{2}}[/tex]
[tex]r=\sqrt{100}[/tex]
r = 10
Now, find θ:
[tex]$\tan \theta=\frac{y}{x}[/tex]
[tex]$\tan \theta=\frac{6}{8}[/tex]
Cancel the common factor 2.
[tex]$\tan \theta=\frac{3}{4}[/tex]
[tex]$\theta=\tan^{-1} \left(\frac{3}{4}\right)[/tex]
θ = 36.87°
The polar coordinates are (r, θ) = (10, 36.87°).
