Question

Determine two pairs of polar coordinates for the point (3, -3) with 0° ≤ θ < 360°.

choices:
(3 , 315°), (-3 , 135°)

(3 , 225°), (-3 , 45°)

(3 , 45°), (-3 , 225°)

(3 , 135°), (-3 , 315°)

Answer 1

Is the given point (3, -3) in polar form? or cartesian form?

Answer 2

polar

Answer 3

ok so I'm guessing that (3, -3) means r = 3 and theta = -3 radians right?

Answer 4

or I guess theta = -3 degrees

not exactly sure

Answer 5

it would be degrees

Answer 6

ok well -3 degrees is coterminal to 360 - 3 = 357 degrees

Answer 7

wait but thats not on there.. lol

Answer 8

hmm let me think for a sec

Answer 9

okay haha

Answer 10

something seems to be missing

a symbol maybe

can you post a screenshot of the entire problem please?

Answer 11

i have no idea how to screen shot lol

Answer 12

above the insert key is the print screen key

Answer 13

on your keyboard

Answer 14

but i copy and pasted it word for word and i checked and no symbols are missing

Answer 15

hit that button

then open up MS paint

paste it in

save it, post it

Answer 16

oh my gosh i feel like an idiot.. there is something missing

Answer 17

im sorry let me fix it

Answer 18

that's ok, and the site is going verrry slow for me lol, so fair warning

Answer 19

hopefully you figured out how to take a screenshot

Answer 20

\[(3 \sqrt{2,} 315°), (-3\sqrt{2} , 135°)\]

\[ (3\sqrt{2} , 225°), (-3\sqrt{2} , 45°) \]
\[ (3\sqrt{2} , 45°), (-3 \sqrt{2}, 225°)\]

\[ (3\sqrt{2} , 135°), (-3 , 315°)\]

Answer 21

oh ok, those are the answer choices?

Answer 22

oh the last one is \[ (3 \sqrt{2}, 135°), (-3\sqrt{2} , 315°)\]

Answer 23

yes, my bad

Answer 24

alright, that's ok and thx

Answer 25

does that make more sense?

Answer 26

if the given point is in cartesian form, then

r = sqrt(x^2 + y^2)

r = sqrt(3^2 + (-3)^2)

r = sqrt(9 + 9)

r = sqrt(18)

r = 3*sqrt(2)

Answer 27

the angle is

theta = arctan(y/x)

theta = arctan(-3/3)

theta = arctan(-1)

theta = -45 which is coterminal to 360 + (-45) = 315 degrees

Answer 28

now if you add 180 degrees to this, you basically make r negative (because you're going in reverse now)

so

315 + 180 = 495

which is coterminal to 495 - 360 = 135 degrees

Answer 29

oh so it's the first!

Answer 30

so yep, it's A

Answer 31

thank you so much i really appreciate the help!

Answer 32

yw

Answer 33

oh wait i lied..
lol im sorry! hold on let me fix the choices!