Question

Find all polar coordinates of point P = (6, 31°)

Answer 1

@Kainui @freckles @TheSmartOne

Answer 2

@robtobey

Answer 3

can you find one that is equivalent where r is negative ?

Answer 4

no, i don't believe so

Answer 5

do you know how to graph polar coordinates?
say if I asked you to graph for example (2,30 degs) and (-2,-150 degs) or (-2,210 degs)
could you plot these?
and if so what do you notice about all 3 points?

Answer 6

thats the part im struggling with, we learned it in class today but i didnt fully grasp how to do it

Answer 7

say I want to graph (2, 30 deg)
30 degrees is in the first quadrant
and we are going to stay in the first quadrant because r is 2
r=2 means we are going to a distance of 2 from the center at a 30 degree angle formed from the x-axis there

Answer 8

so I drew a point on the second ring
where I have 30 degrees formed by the initial ray (the x-axis) and a line segment if I were to draw one from (0,0) to that dot there on the second ring

Answer 9

now if I were to plot (-2,210 deg)
find the angle first
and then use the r to go in the direction or the opposite direction of
and also use r to figure out which ring to use (this ring symbolize the distance from the origin)

Answer 10

so since we have 210 degrees that means we are going to be somewhere on that line where I drew that first point (2,30 deg)
the negative means we are going to go the opposite direction of the angle
and we have |r|=2 so we are going to still be on the 2nd ring
this means (-2,210 deg)=(2,30 deg)

Answer 11

(-2,-150 deg) also equals (2,30 deg)
and so on....

Answer 12

there are infinitely many ways to name that point (2,30 deg)

Answer 13

you can keep going around the circle infinitely many times to by just changing theta and using the period of cosine or sine function
or
you can change the sign of r and use the the angle +180 deg and keep going around the circle infinitely times after that

Answer 14

ok, yeah that is making a lot more sense than it was in class. I understand how it goes out from center on the first number and the second number tells me at what angle i can place it. But that also means there are a lot of different ways to name the same point. Am i understanding that right?

Answer 15

yes infinitely many ways

Answer 16

you will need to use k
to represent any integer

Answer 17

or whatever variable you want to represent an integer
just make sure you define it as any integer

Answer 18

ok, i can see that. Now how would i go about doing the problem that I proposed. I get that there are infinitely many ways, but the question i am answering says to give all. How do I do that?

Answer 19

\[(r,\theta)=(r,\theta+360^ \circ k) \\ (r,\theta)=(-r,(\theta+180^\circ)+360^\circ k)\]
this is what I was saying in words

Answer 20

again the answer to that question is you are going to have to use some number to represent any integer

Answer 21

oh yeah, i see what youre saying since you wrote it out

Answer 22

so would my answer be:
(r,θ)=(6,31+360∘k)
(r,θ)=(−6,(31+180∘)+360∘k)

Answer 23

you can add the 31 and 180 to simplify things

Answer 24

So just:
(r,θ)=(6,31+360∘k)
(r,θ)=(−6,(221∘)+360∘k)

Answer 25

(r,θ)=(6,31+360∘k)
(r,θ)=(−6,221∘+360∘k)
I would drop those one ( )
but yeah

Answer 26

ok, awesome thanks so much
could you help me with one more? @freckles