# Math Help - COnverting rectangular equations to polar (and vice versa)

1. ## COnverting rectangular equations to polar (and vice versa)

i understand the concepts of converting single coordinates, however im confused on how and why on some these parts.... hopfully i could get a little more help on this...

Convert equations to rect.

r=4

$rsin(\theta) = -2$

$\theta = pi/3$

$r = sin(\theta) - cos (\theta)$

Convert Equations to polar

$2x^2 + 2y^2 = 3$
$y = 3$

I already got a hang of some of the basics of this... but a little further explanation owuld be much appreciated so i can hopeuflly ace this coming quiz. ty

2. the relation between polar and rectangle:

$x = r \cos (\theta)$
$y = r \sin (\theta)$
$r^2 = x^2 + y^2$

for example:

$2x^2 + 2y^2 = 3
$

$2(x^2 + y^2) = 3$
$2r = 3$
$r=\frac {3}{2}$

4. ok, this is more of the material my teacher wants.... can anyone please check on correctness and help me fix my errors.

: y=1.732x using tan(y/x)

: $r^2 = y^2 - x^2$

$rsec(\theta) = -4$

-4 = x

$r = cos(\theta)$

y=x

Convert Equations to polar

===> $2cos(\theta)^2 + 2sin(\theta)^2 = 3
$

please tell me whats right, whats right, and what i can fix.

$y = -3 \longrightarrow sin^2 = - 3$