The components of Vector A are given as follows

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Homework Help Overview

The problem involves determining the angle of a vector based on its components, specifically in the context of vector A with given components Ax and Ay. The discussion centers around the calculation of the angle measured counterclockwise from the x-axis and the implications of quadrant placement on angle determination.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the method of using arctan to find the angle and question the necessity of adding 360 degrees for counterclockwise measurements. There are considerations about quadrant placement and how it affects angle calculations, including the use of sketches to visualize the vector's position.

Discussion Status

The discussion is active with various interpretations being explored regarding angle calculation and quadrant considerations. Some participants provide insights into the limitations of the arctan function and how to adjust angles based on the quadrant in which the vector lies.

Contextual Notes

Participants note that the arctan function typically produces angles within a limited range, which may necessitate adjustments to find the correct angle representation based on the vector's quadrant. There is an ongoing exploration of how to handle angles measured in different directions (clockwise vs. counterclockwise).

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Homework Statement


The components of Vector A are given as follows

Ax=+3.9

Ay=-4

The angle measured counterclockwise from the x-axis to vector A , in degrees, is closest to:


Homework Equations


arctan(y/x)= theta


The Attempt at a Solution



Hey guys, I got the answer doing Arctan (-4/3.9) +360

My question is how do we know to add 360? Do we always add 360 when it is counterclockwise to the x-axis? and what about if they asked if it was clockwise to the x-axis or vica versa for the Y axis, would we have to treat it any different.

Thank you
 
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Personally, I would make a sketch to see what quadrant the vector is in. Then add 90, 180 or 270 degrees to whatever the calculator said in order to get the angle in the correct quadrant.
 
Would it have anything to do since Tan is positive in quadrant four they add 360 to get an answer in quadrant four?
 
The xy coordinates/components gave you a line in the 4th quadrant. In a calculator, arctan will always produce an angle between ∏/2 and -∏/2. Thus, the arctan in a calculator can not produce an angle greater than 90 degrees, so if your line is in the 4 quadrant, arctan in a calculator will provide the angle between 90 and -90. And that happens to be a negative angle. If you want the positive version of that angle, you will have to go around like a clock one full turn to get the other angle that matches the position of your line.

If that didn't make sense, I am sorry and don't worry, someone will come by and provide a clearer explanation.
 

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