Question

D

Answer 1

uh

still working on this one

but I believe you would start with y = r*sin(theta) and try to re-write rcsc(theata) = 8 in terms of y only

Answer 2

alright I think I got it

converting csc to sin gives us

r/sin(theta) = 8

multiply the numerator and the denominator by r gives us

r^2/rsin(theta) = 8

r^2 = x^2 + y^2 using the polar to rectangular conversion
rsin(theta) = y using that same reasoning, so

(x^2 + y^2) / y = 8

multiply both sides by y then complete the square on the y-terms to get the solution

Answer 3

A

Answer 4

hm, try one more time, notice how (x^2 + y^2) / y = 8 has an x term in it

Answer 5

so either c or d

Answer 6

multiplying both sides by y gives us

x^2 + y^2 = 8y

subtracting 8y from both sides:

x^2 + y^2 - 8y = 0

try completing the square on the y terms

Answer 7

C

Answer 8

as a review: to complete the square, start with the coefficient on the y term (not the y^2 term, the y term) , divide by 2, square the result, then add that to both sides

Answer 9

B

Answer 10

:/

Answer 11

good

Answer 12

True

Answer 13

good

Answer 14

B and D

Answer 15

B is good, D does not work because it doesn't have radial symmetry (not all the points are the same distance from the origin)

Answer 16

A

Answer 17

well i guess c

Answer 18

if B is true then C is automatically false

A doesn't work either because it's not symmetric about that line

Answer 19

D

Answer 20

good

Answer 21

C

Answer 22

A

Answer 23

good

Answer 24

D

Answer 25

it's probably not a line (polar graphs tend to produce curved/rounded images)

any attempts to graph this? https://www.desmos.com/calculator/ms3eghkkgz

Answer 26

limacon

Answer 27

good

Answer 28

A

Answer 29

not quite

as a hint, graphing the coordinates gives more of a ~heart~ shape

Answer 30

D

Answer 31

excellent

Answer 32

that's the same question

Answer 33

polar

Answer 34

good

Answer 35

C

Answer 36

Actually D :/

Answer 37

check the image file again

Answer 38

C

Answer 39

you reposted the same image about the polar coordinates question

Answer 40

sorry

Answer 41

this may be circle i tink

Answer 42

had to look this one up but since we only have a theta value (no r) we assume this is a straight line with theta = -pi/6 and r being any arbitrary number

Answer 43

A

Answer 44

good

Answer 45

B

Answer 46

very close but since we have an odd # of petals the (ntheta) has to be odd

Answer 47

A

Answer 48

good