Calculating polar coordinates

Homework Statement

B⃗ = -2.0ι^ + 3.0 j^.
Find the polar coordinates r and theta.

n/a

The Attempt at a Solution

r=sqrt((-2.0)^2+(3.0^2))
r = 3.6

theta = tan^-1(3/-2) = -56 degrees

The answers seem to be wrong, can I get any guidance on this question please?

Draw a picture. Where is the Cartesian point? Why doesn't your angle make any sense?

Flinze
Draw a picture. Where is the Cartesian point? Why doesn't your angle make any sense?

Oh it's in the second quadrant, I see how the angle wouldn't work. So would it then be +56 degrees?

haruspex
Homework Helper
Gold Member
Oh it's in the second quadrant, I see how the angle wouldn't work. So would it then be +56 degrees?
Is that in the correct quadrant?
Do you know what the graph of tan looks like? If you put a horizontal line through it at a random height, what can you say about the intercepts?

Flinze
Is that in the correct quadrant?
Do you know what the graph of tan looks like? If you put a horizontal line through it at a random height, what can you say about the intercepts?
I believe it is on the correct quadrant as -x,+y = quadrant 2. And there should only be one intercept I believe?? I'm confused

SteamKing
Staff Emeritus
Homework Helper
Oh it's in the second quadrant, I see how the angle wouldn't work. So would it then be +56 degrees?
Where is zero degrees located?
How many degrees in each quadrant?

Flinze
Where is zero degrees located?
How many degrees in each quadrant?
Quadrant I, and III have positive angles I believe There are 90 degrees in each quadrant, and zero is located on the x-axis on quadrant I.

SteamKing
Staff Emeritus
Homework Helper
Quadrant I, and III have positive angles I believe There are 90 degrees in each quadrant, and zero is located on the x-axis on quadrant I.
Well 2 out of 3 isn't bad, but it should be three out of three in this case.

If you start at zero degrees and go counterclockwise to 180 degrees, which quadrants have positive angles?

If you start at zero degrees and go clockwise to 180 degrees, which quadrants have negative angles?

The tricky thing about arctan on your calculator is it returns an angle θ such that -π/2 ≤ θ ≤ π/2, and the user is left with deciding in which quadrant the proper angle falls and its measure from zero degrees. That's why you should plot the original cartesian coordinates.

Flinze
haruspex
Homework Helper
Gold Member
I believe it is on the correct quadrant as -x,+y = quadrant 2. And there should only be one intercept I believe?? I'm confused
Sure, but +56 degrees is not in that quadrant.
For the intercepts, what range of angles did you consider in saying there is only one intercept?

Flinze
Well 2 out of 3 isn't bad, but it should be three out of three in this case.

If you start at zero degrees and go counterclockwise to 180 degrees, which quadrants have positive angles?

If you start at zero degrees and go clockwise to 180 degrees, which quadrants have negative angles?

The tricky thing about arctan on your calculator is it returns an angle θ such that -π/2 ≤ θ ≤ π/2, and the user is left with deciding in which quadrant the proper angle falls and its measure from zero degrees. That's why you should plot the original cartesian coordinates.

Quadrant I would be positive for the first part, and Quadrant IV would be negative on the second question.
So then what I would do is 180-54=124?

Sure, but +56 degrees is not in that quadrant.
For the intercepts, what range of angles did you consider in saying there is only one intercept?
The answer -56 would be in quadrant IV and +56 would be in quadrant one then right?

SteamKing
Staff Emeritus