Question

HELP
r = -6 sin(theta)

Part I: Multiply both sides of this equation by r and use the fact that to rewrite this equation in terms of x and y.

Part II: Complete the square to produce the final equation.

Part III: Using only your answer to part II, what shape does this graph make?

Answer 1

\[ \sin \theta = \frac y r \text{ and } r = \sqrt{x^2 + y^2 }\]
put those values and simplify them, you will get an circle

Answer 2

\[ x^2 + (y^2 + 6y + 9) - 9 \]
also make square by adding 9, other 9 goes to left, giving you radius of 9

Answer 3

*right

Answer 4

http://www.wolframalpha.com/input/?i=polar+plot+r%3D-6sin \theta

Answer 5

why do u add 9?

Answer 6

add +9 ... also add -9 to balance them,

Answer 7

so that you can make
\[ x^2 + (y+3)^2 - 9 = 0\]

Answer 8

sso that would be the answer for tpart b?

Answer 9

i still a little unclear on part a

Answer 10

@experimentX

Answer 11

what part a and b?? i see i ii iii

Answer 12

im sorry i meaqnt i and ii

Answer 13

1) just substitute those values of sin \theta (first) then multiply by r on both sides, then put the values of r ..
check out my first post for that

Answer 14

2) from 1) you will be getting \( x^2 + y^2 + 6y = 0 \)
completing squrares meand making of this form
\( x^2 + (y+3)^2 - 9 = 0 \) which i did earlier ...

3) or you have \( \( x^2 + (y+3)^2 = 3^2 \) and if you remember corrrectly the standard equationf o circle, it's a circle with center 0, -3 and radius 3

Answer 15

would x be -6 and y be 1?

Answer 16

?? x is never -6

Answer 17

plugin those values to see if it satisfies that equation or not