Vector Components and Finding the Angle

In summary, the angle theta for a vector with components A_x = -4.50m and A_y = -3.30m is 36.25 degrees. However, the correct way to determine the angle is by measuring counterclockwise from the +x-axis and adding 180 degrees to the original answer of 36.25 degrees. This gives an angle theta of 216.25 degrees.
  • #1
Soaring Crane
469
0
Let the angle theta be the angle that the vector A makes with the +x-axis, measured counterclockwise from that axis. Find the angle theta for a vector that has the following components:

A_x = -4.50m
A_y = -3.30m

Using the calculator, I got arctan(-3.30m/-4.50 m) = 36.25 degrees.

However, this answer is wrong. I know the angle is supposed to be counterclockwise from +x-axis, but I thought the signs canceled out. What is the correct way of determining the angle?

Thanks.
 
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  • #2
your answer is right, but your frame of reference is off.

where is an angle theta equal to 0 at? think about how the problem stated the increase in theta.

did you draw a picture?
 
  • #3
Well, I drew vector A in quadrant 3 and subtracted the angle from 270 (270 - 36.25 = 234), but that answer is wrong.
 
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  • #4
Soaring Crane said:
Well, I drew vector A in quadrant 3 and subtracted the angle from 270 (270 - 36.25), but that answer is wrong.
You should be measuring anti clockwise, add 180o to your original answer.
 

FAQ: Vector Components and Finding the Angle

1. What are vector components?

Vector components are the individual parts of a vector that describe its magnitude and direction. They are usually represented by the x and y coordinates in a two-dimensional space.

2. How do you find the magnitude of a vector's components?

The magnitude of a vector's components can be found using the Pythagorean theorem, which states that the magnitude (M) is equal to the square root of the sum of the squares of the individual components (x and y).

3. How do you find the angle of a vector's components?

The angle of a vector's components can be found using trigonometric functions. The tangent of the angle is equal to the ratio of the y component to the x component, and the inverse tangent can be used to find the angle.

4. Can vector components be negative?

Yes, vector components can be negative. This indicates that the vector is pointing in the opposite direction of the positive component. For example, a vector with an x component of -5 and a y component of 3 would have a direction of 180 degrees (or pi radians).

5. How do you add and subtract vectors using their components?

To add or subtract vectors using their components, you simply add or subtract the corresponding x and y components to get the resulting vector. This is known as the component method and is often used in physics and engineering applications.

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