Question

Explain polar coords and give an example.

Answer 1

With rectangular coords we typically represent locations as the intersection of lines on a horizontal/vertical axes. With polar coords, we take the magnitude of the x and y parts that we are used to on a cartesian coord system. so if we had a point (3,4), to find the magnitude we would just that the square root of (3^2 + 4^2). Just think of it like finding the hypotenuse if you were doing pythagorean theoram. What you now have, in polar, is rhe "r", which is just the length of the ray (line) from the origin (0,0). But, we also need something else called the argument, which is the angle (or theta) from the x-axis.

If we had some point on the cartesian plane, like (1,1) then it would have an "r" of sqrt(2), and an argument of pi/4. I would write it like sqrt(2)[cos(pi/4) + sin(pi/4)]. You might also be able to write it like sqrt(2)*e^i*(pi/4).

Answer 2

What is the Cartesian Plane?

Answer 3

just the normal x,y coords that we are used to.

Answer 4

Okay.

Answer 5

Where did you get the r's from (1,1)?

Answer 6

if I take the sqrt of 1^2 + 1^2, I have sqrt(2). Just think of it like finding the hypotenuse of a right triangle.

Answer 7

So if this (1,1) was (x,y), then it is x^2+y^2?

Answer 8

Or the sqrt(x^2+y^2)?

Answer 9

with x,y coords we look for whee they intersect and that is the point. with polar, we have a ray that extends from the origen. the length of that ray is found just by the same way that you would find the hyp of a right triangle.

Answer 10

sqrt(x^2 + y^2)

Answer 11

Oh! Okay, thanks!

Answer 12

remember, that just gives you the length of the ray from the origin. You still need to include an angle, or else we would have no idea where the endpoint of the ray is.

Answer 13

Wait, so how do I get the angle?

Answer 14

You will likely have to use your trig and the length of the x (cosine) and y (sine) parts to determine angle. If you have an angle that can be represented at y/x, then you also have something that can be represented as tangent theta, right? (because sin/cos). So once you have that, then you take the arctan (y/x) and that will give you the angle.

Answer 15

so for the example I used above, if I have x = 1 and y = 1, then what I really have is y/x = 1/1 = 1. So I take tangent theta = 1, ----> theta = arctan (or tan inverse) (1), and that is pi/4 (or 45 degrees if you are in degree mode)

Answer 16

Can you help me with this problem? I think it might be simpler to explain the steps. Use your grapher to determine which of the graphs matches the polar equation r = 3 sin 2θ.

Answer 17

what is the theta?

Answer 18

IT says 3 sin 2(theta)

Answer 19

Without rectangular coords to convert to polar, or a polar coord to convert back to rectangular, I'm not really sure what to do with that. Where are the graphs the question is asking you to compare it to?

Answer 20

The answer choices?

Answer 21

yeah

Answer 22

ah, ok. hold on, let me plot it.

Answer 23

it is the third option

Answer 24

How did you get that?

Answer 25

do you have a graphing calculator? On mine, I switched the graph-type from rectangular to polar, then I just entered what you gave me: 3sin(2theta). It plotted the 3rd option.

Answer 26

Oh, okay.

Answer 27

Can you do another one? Find the rectangular coordinates of the point with the polar coordinates (8,3/2*pi ).

Answer 28

My calculator isn't cooperating, but lets see if we can reason the answer. We know r=8, and we have a theta of 3/2*pi. So I think then that the point is on the y-axis below zero. We have a problem trying to use tangent right away, because cosine of (3/2*pi) = 0, that means tangent give a divide by zero error. Even so, we know the ray is length 8, so I think the rectangular coords are (0,-8)

Answer 29

Okay,

Answer 30

That's an answer! gj!

Answer 31

Wait, can I try one, and tell me if it's correct/

Answer 32

Sure

Answer 33

Find the rectangular coordinates of the point with the polar coordinates . This is the question.

Answer 34

(-3, 5pi/8)

Answer 35

Those are the coords.

Answer 36

So r=-3, right?

Answer 37

Agh, I'm confused.

Answer 38

r = -3, but remember that r is sqrt(x^2 + y^2). We get the negative sign because 5/8*pi is in quadrant II, which means the cosine (x) part is a negative number.

Answer 39

So I will need a unit circle, right?

Answer 40

That is probably what I would do, look at tan(5/8pi) first

Answer 41

It's not on the unit circle.

Answer 42

if you divide pi (the top half of the circle) into 8, you can see that 5/8pi is just a little past pi/2

Answer 43

So pi/2?

Answer 44

0,1

Answer 45

what I did to find x was 3cos(5/8*pi), and to find y was 3sin(5/8*pi). I had to round off a bit, but I got x = 1.15 and y = -2.78. Just to doublecheck, I did sqrt((1.15)^2 + (-.2.78)^2) and it did come back as 3.

Answer 46

Since 5/8pi is in quadrant 2, I know the x value must be negative, and the y value will be positive.

Answer 47

Can you tell me the equation you useed>

Answer 48

I only used what you gave me. So, my reasoning went like this: first, locate what quadrant 5/8*pi is located. It is in Q2, so we are dealing with a negative x and a positive y. Then, to find x, I just entered 3cos(5/8*pi) into my calculator and got -1.15 (rounded). To find y, I entered 3sin(5/8*pi) into my calculator, and it gave me 2.78 (rounded). So with that I now have my x and y values to plot.

Answer 49

So for r, you used x(sin or cos) of y, right?

Answer 50

Yes, but I just thought of something. If that r is -3, then I should have used it in my computations for x and y, which would have switched the signs of both x and y. I think we need to change my answer to 1.15 and -2.78, sorry about that.

Answer 51

So x =-2.78?

Answer 52

nope, x = 1.15, and y = -2.78. Cosine gives us the x part, and Sine gives us the y part.

Answer 53

Wait, I thought x was negative.

Answer 54

it was, but look at that r. r = -3, so we have to include that in our calculation. If we have some negative value for x and multiply by -3, the answer will turn positive, right?

Answer 55

Oh, okay.

Answer 56

But I don't have that answer choice.

Answer 57

same for y. It would be positive, but times -3 it turns negative.

Answer 58

what are the options?

Answer 59

I only have (-3/2,3/2) (3sqrt(3)/2),-3/2) (-3/2, 3sqrt(3)/2) and 3/2, -3/2

Answer 60

Hello?

Answer 61

I need to leave in half an hour, with the assignment done and Istill dont understand polar coords. I'm osrry, but I need a brief descriptiion that wil help get my assignment done.

Answer 62

@satellite73 Please help!

Answer 63

It looks like there is probably a much easier/better way to do this problem than how I've been working on it. You might be better off spending that 30 minutes reviewing the textbook or getting help from someone better at this than I am.

Answer 64

Soeey Ajk, maybe someome else can explani it better.

Answer 65

Thanks anyway.

Answer 66

:(

Answer 67

@cwrw238

Answer 68

@dpaInc

Answer 69

I'd be interested to see an explanation, if someone else helps. I'll check back and hopefully learn something too.

Answer 70

@satellite73

Answer 71

@dpaInc