Question

sketch the curve with the given polar equation by first sketching the graph of r as a function of theta in Cartesion coordinates. r=-2sin(theta)

Answer 1

this is one way to do it:

multiply both sides by r where r=/= 0

\[r^2 = 2rsin(\theta)\]
use the fact that r^2 = x^2 + y^2 = r^2 and that rsin(theta) = y

so your equation is:\[x^2 + y^2 = 2y\]\[x^2 + y^2 - 2y = 0\]

you'll want to complete the square to get it in the general form of a circle equation.

should i keep going or should i leave you the fun part?

Answer 2

can you please keep going?

Answer 3

completing the square:\[x^2 + y^2 - 2y = 0\]\[x^2 + [(y - 1)^2 - 1] = 0\]\[x^2 + (y -1)^2 = 1\]
the general equation of a circle:\[(x - h)^2 + (y - k)^2 = r^2\]where r is the radius and the center of the circle is the point (h, k)

in our case, we have a circle of radius 1 centered at (0, 1).

do you know how to you draw it?

Answer 4

not really

Answer 5

wait is r=-2 sin theta

Answer 6

my drawing was wrong, sorry.

it doesn't doesn't change much though

-y = -rsin(theta)

so we have

x^2 + y^2 + 2y = 0


we end up with:

x^2 + (y + 1)^2 = 1

this would be centered at (0, -1)

Answer 7

i hope this helps. re-reading it might help if it didn't.

i have to go make food; starving!

Answer 8

thank you so much