A community for students.
Here's the question you clicked on:
 0 viewing
LordVictorius
 2 years ago
Explain polar coords and give an example.
LordVictorius
 2 years ago
Explain polar coords and give an example.

This Question is Closed

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2With 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 xaxis. 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).

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0What is the Cartesian Plane?

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2just the normal x,y coords that we are used to.

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0Where did you get the r's from (1,1)?

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2if 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.

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0So if this (1,1) was (x,y), then it is x^2+y^2?

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0Or the sqrt(x^2+y^2)?

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2with 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.

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0Oh! Okay, thanks!

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2remember, 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.

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0Wait, so how do I get the angle?

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2You 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.

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2so 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)

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0Can 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.

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0IT says 3 sin 2(theta)

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2Without 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?

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0The answer choices?

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2ah, ok. hold on, let me plot it.

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0How did you get that?

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2do you have a graphing calculator? On mine, I switched the graphtype from rectangular to polar, then I just entered what you gave me: 3sin(2theta). It plotted the 3rd option.

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0Can you do another one? Find the rectangular coordinates of the point with the polar coordinates (8,3/2*pi ).

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2My 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 yaxis 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)

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0That's an answer! gj!

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0Wait, can I try one, and tell me if it's correct/

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0Find the rectangular coordinates of the point with the polar coordinates . This is the question.

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0Those are the coords.

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0Agh, I'm confused.

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2r = 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.

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0So I will need a unit circle, right?

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2That is probably what I would do, look at tan(5/8pi) first

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0It's not on the unit circle.

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2if you divide pi (the top half of the circle) into 8, you can see that 5/8pi is just a little past pi/2

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2what 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.

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2Since 5/8pi is in quadrant 2, I know the x value must be negative, and the y value will be positive.

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0Can you tell me the equation you useed>

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2I 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.

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0So for r, you used x(sin or cos) of y, right?

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2Yes, 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.

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2nope, x = 1.15, and y = 2.78. Cosine gives us the x part, and Sine gives us the y part.

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0Wait, I thought x was negative.

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2it 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?

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0But I don't have that answer choice.

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2same for y. It would be positive, but times 3 it turns negative.

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0I only have (3/2,3/2) (3sqrt(3)/2),3/2) (3/2, 3sqrt(3)/2) and 3/2, 3/2

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0I 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.

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0@satellite73 Please help!

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2It 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.

LordVictorius
 2 years ago
Best ResponseYou've already chosen the best response.0Soeey Ajk, maybe someome else can explani it better.

Ajk
 2 years ago
Best ResponseYou've already chosen the best response.2I'd be interested to see an explanation, if someone else helps. I'll check back and hopefully learn something too.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.