The discussion focuses on converting the Cartesian coordinates of the vector B⃗ = -2.0ι^ + 3.0 j^ into polar coordinates, specifically calculating the radius (r) and angle (θ). The correct radius is determined to be r = 3.6, while the angle θ is clarified to be 124 degrees after recognizing that the vector lies in the second quadrant. Participants emphasize the importance of visualizing the Cartesian point and understanding the behavior of the arctangent function to correctly identify the angle's quadrant.
PREREQUISITESStudents studying physics or mathematics, particularly those learning about vector analysis and coordinate transformations.
brainpushups said:Draw a picture. Where is the Cartesian point? Why doesn't your angle make any sense?
Is that in the correct quadrant?Flinze said:Oh it's in the second quadrant, I see how the angle wouldn't work. So would it then be +56 degrees?
I believe it is on the correct quadrant as -x,+y = quadrant 2. And there should only be one intercept I believe?? I'm confusedharuspex said: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?
Which quadrants have positive angles?Flinze said:Oh it's in the second quadrant, I see how the angle wouldn't work. So would it then be +56 degrees?
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 said:Which quadrants have positive angles?
Where is zero degrees located?
How many degrees in each quadrant?
Well 2 out of 3 isn't bad, but it should be three out of three in this case.Flinze said: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.
Sure, but +56 degrees is not in that quadrant.Flinze said: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 said: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.
The answer -56 would be in quadrant IV and +56 would be in quadrant one then right?haruspex said: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?
You're still guessing here. I don't know why you won't plot the original cartesian coordinates. That would answer your question directly.Flinze said:The answer -56 would be in quadrant IV and +56 would be in quadrant one then right?
It would be in quadrant II after I plot (-2,3). Would the angle I be measuring start from the x-axis from quadrant I though?SteamKing said:You're still guessing here. I don't know why you won't plot the original cartesian coordinates. That would answer your question directly.
Never mind, I figured it out, I subtracted 180 with 56 = 124 degrees. Thanks.Flinze said:It would be in quadrant II after I plot (-2,3). Would the angle I be measuring start from the x-axis from quadrant I though?