Find polar coordinates (r, θ) of the point.

In summary: Theta can only be in the second or third quadrant. (-5/3)<0 is in the first quadrant, so your answer is in the second quadrant.
  • #1
Gundown64
9
0

Homework Statement



The Cartesian coordinates of a point are given. (3,-5)

(i) Find polar coordinates (r, θ) of the point, where
r > 0 and 0 ≤ θ < 2π.
(ii) Find polar coordinates (r, θ) of the point, where
r < 0 and 0 ≤ θ < 2π.

Homework Equations



r^2=x^2+y^2
tanθ=(y/x) → θ=arctan(y/x)

The Attempt at a Solution



r=√(9+25)=√(34)

θ=arctan(-5/3)

The problem must be in exact terms which typically involves pi (in the problems I have worked at least). Radians and degrees are not allowed as an answer. What is the value for theta? I can't figure out where to go from there. Any help is appreciated. Thanks!
 
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  • #2
Gundown64 said:
The problem must be in exact terms which typically involves pi (in the problems I have worked at least). Radians and degrees are not allowed as an answer.

If radians and degrees are not allowed as an answer, what units IS your angle supposed to be in? Are you sure you don't mean you simply aren't supposed to submit a decimal approximation to the answer? In this case arctan(-5/3) is the best you can do
 
  • #3
Office_Shredder said:
If radians and degrees are not allowed as an answer, what units IS your angle supposed to be in? Are you sure you don't mean you simply aren't supposed to submit a decimal approximation to the answer? In this case arctan(-5/3) is the best you can do

Yes, sorry, that is what I mean. Decimal approximation is not allowed as far as I know and I'm not even aware that leaving it as arctan(-5/3) is allowed. It does not specify, but all the other problems have had pi in the theta value so I have no idea how it is to be submitted. I guess that is more of my own problem than something you guys can help with, but I am unsure on what to do.
 
  • #4
[itex]\displaystyle -\frac{\pi}{2}<\arctan\left(-\frac{5}{3}\right)<0[/itex]

You need to get your answer into the correct quadrant.
 

Related to Find polar coordinates (r, θ) of the point.

What are polar coordinates?

Polar coordinates are a system used to locate points in a two-dimensional plane using a distance (r) and an angle (θ) from a fixed reference point.

What is the reference point in polar coordinates?

The reference point in polar coordinates is called the pole, and it is typically denoted by the letter O.

How do you convert Cartesian coordinates to polar coordinates?

To convert from Cartesian coordinates (x,y) to polar coordinates (r, θ), use the following equations:
r = √(x² + y²) and θ = tan⁻¹(y/x)

How do you plot a point using polar coordinates?

To plot a point using polar coordinates (r, θ), start at the pole and move r units in the direction of θ. The point will be located where you end up.

What is the difference between polar coordinates and Cartesian coordinates?

The main difference between polar coordinates and Cartesian coordinates is the way they represent points in a plane. Polar coordinates use distance and angle, while Cartesian coordinates use x and y coordinates.

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