Question

Convert the rectangular coordinates to polar coordinates with
r > 0 and 0 ≤ < 2.

Answer 1

Answer:

,

$(6, \frac{11\pi}{6} )$

Step-by-step explanation:

Note I'm using a, instead of theta to represent angles.

To convert rectangular to polar, apply these formulas

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

$\alpha = \tan {}^{ - 1} ( \frac{y}{x} )$

Note : Rectangular coordinates are the coordinates you were learning since elementary school or middle school.

The first number is x, and the second is y.

So

$r = \sqrt{(3 \sqrt{3} ) {}^{2} + ( - 3) {}^{2} }$

$r = \sqrt{36}$

$r = 6$

$\alpha = \tan {}^{ - 1} ( \frac{ - 3}{3 \sqrt{3} } )$

Since our y coordinate is negative and x coordinate is Positve , on the unit circle, the angle must be in the fourth quadrant.

So the angle must be in between

$\frac{3\pi}{2} < \alpha < 2\pi$

$\alpha = \tan {}^{ - 1} ( \frac{ - 1}{ \sqrt{3} } )$

$\alpha = \frac{11\pi}{16}$

So our answer is

(6, 11pi/6).