Help with Rectangular and Polar equations

Question

darkbluechocobo · Answer

Convert the following expression into an equivalent rectangular expression: r = 4sinθ

darkbluechocobo · Answer

well the center of a circle is (b/2,90degrees) so 4/2=2 so (2,90)

darkbluechocobo · Answer

we can use x=rcosTheta and y=rsinTheta

darkbluechocobo · Answer

is r 2?

phi · Answer

the circle has a radius of 2 and center (0,2)

darkbluechocobo · Answer

How did you get the center?

phi · Answer

you could do this
$$ r = 4 \sin \theta \ r^2 = 4 r \sin \theta 
$$
use  $$ r^2 = x^2 + y^2 \ y = r \sin \theta$$
to get
$$ x^2 + y^2= 4y$$

phi · Answer

complete the square on the y's to get
$$ x^2 + y^2-4y= 0 \ x^2 + y^2 -4y +4 = 4\
x^2+ (y-2)^2 = 4 
 $$

darkbluechocobo · Answer

Wow that's a lot simpler than the method I was using

darkbluechocobo · Answer

Say we had r=5? Could you just do x^2+y^2=5^2

darkbluechocobo · Answer

r=-5*

darkbluechocobo · Answer

That would leave us with x^2+y^2=25? would that be an example of this method?

anonymous · Answer

r = 4 sin theta, the minimum value is when theta =0, r =0. In polar r is a length, can't be negative, the negative sign is to show how the angle is.

anonymous · Answer

in your case, maximum value of r is 4 , since $-1\leq sin\theta\leq 1$,

phi · Answer

***Say we had r=5? Could you just do x^2+y^2=5^2***
yes. in polar coords, r=5 is the circle with center (0,0) and radius 5
in rectangular coords, that would be  x^2 + y^2 = 25