Solving Vector B in Polar Notation: -3.85 and -4.59?

In summary, the given vector B in polar notation (6,-130degrees) can be converted into rectangular notation by using the relation between polar and rectangular coordinates. The resulting values for x and y may differ from the given answer of -3.85 and -4.59, which could be due to the restriction of angles between -180 and +180. Using calculators to solve such problems may not help in understanding the concept fully.
  • #1
ramman1505
3
0

Homework Statement


Vector B is given in polar notation as (6,-130degrees). In rectangular notation vector B is what?


Homework Equations


For this problem, take all angles between -180 and +180.


The Attempt at a Solution



I got an answer or -3.85 and -4.59. However they were the wrong answers. I suspect it has something to do with the all angles between -180 and +180 part. I took (6,50degrees) and put it in the calc. and got that answer -3.85 and -4.59. What am i doing wrong?
 
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  • #2
What exactly did you do?
 
  • #3
I put [6,50degrees] in the calculator and solved it for rectangular notation. Which should give me the x and y values of the rectangular notation.
 
  • #4
ramman1505 said:
I put [6,50degrees] in the calculator and solved it for rectangular notation. Which should give me the x and y values of the rectangular notation.

If you use calculators to solve your problems, you'll never know how to solve them, right? So, what is the relation between polar and rectangular coordinates?
 

1. What is vector B in polar notation?

Vector B in polar notation is a way of representing a vector in terms of its magnitude and direction. It is expressed as (r, θ), where r is the magnitude and θ is the direction in degrees or radians.

2. How do you solve for vector B in polar notation?

To solve for vector B in polar notation, you will need to use trigonometric functions. First, find the magnitude of the vector by using the Pythagorean theorem: √((-3.85)^2 + (-4.59)^2) = 6.06. Then, use inverse trigonometric functions to find the direction in degrees or radians: θ = tan^-1(-4.59/-3.85) = 51.7° or 0.90 radians.

3. What does a negative magnitude in vector B mean?

A negative magnitude in vector B means that the vector is pointing in the opposite direction of the positive direction. In polar notation, the direction is given as an angle between 0 and 360 degrees or 0 and 2π radians, with 0 degrees or 0 radians being the positive x-axis. In this case, the vector is pointing in the third quadrant, 180-360 degrees or π-2π radians.

4. What is the difference between polar and Cartesian coordinates?

Polar coordinates use magnitude and direction to represent a point or vector, while Cartesian coordinates use x and y coordinates. In polar notation, the direction is given as an angle, while in Cartesian coordinates, it is given as the slope of the line. Polar coordinates are often used when dealing with circular or rotational motion, while Cartesian coordinates are used for linear motion.

5. How can vector B be converted to Cartesian coordinates?

To convert vector B from polar to Cartesian coordinates, you can use the following formulas: x = r cos(θ) and y = r sin(θ). In this case, x = 6.06 cos(51.7°) = -3.85 and y = 6.06 sin(51.7°) = -4.59. This means that vector B in Cartesian coordinates is (-3.85, -4.59).

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