Angle of vevtor in component form

[arukia]

Angle of vector in component form

Find the vector's magnitude and direction. Use right as the +x direction and up as the +y direction.

$\vec{A} = 3.50 \hat{i} - 7.70 \hat{j}$

Find $\theta_A$ degrees below the positive x-axis.

$\theta_A = arctan\left ( \frac{7.70}{3.50} \right )$

$=65.55604522^\circ$

$360^\circ - 65.55604522^\circ = 294.4439548^\circ$

But this is wrong. I also tried: -65$^\circ$ and 336$^\circ$

 

[BruceW]

Usually the angle is measured anticlockwise from the x axis, in which case your answer of 294.44 degrees would be correct. When you found the angle below the positive axis, that was an intermediate step? Or is that what the question asked you for? If the question asked for that, then the answer would be 65.56 degrees.

 

[arukia]

No my 294$^\circ$ was the final answer and what was being asked.
Yes, 65$^\circ$ turned out to be correct but I don't understand why.
Since the question asked: Find $\theta_A$ degrees below the positive x-axis. I thought it would be -65$^\circ$ or 294$^\circ$
By the way are links to a non-copyrighted PDF allowed in the forums ?

 

[BruceW]

I'm not sure about the PDF's... I would suppose so. About the problem, they ask for degrees below the positive x-axis, so this means the angle as measure clockwise from the x-axis, which is why the answer is +65 degrees. In the usual convention of measuring anti-clockwise, the answer would have been 294 degrees, but they specify to not use the convention.

 

[asteriatic]

The angle of the vector in component form can be found using the inverse tangent function. In this case, the angle is found to be 65.55604522 degrees below the positive x-axis. However, it is important to note that the direction of the angle can vary depending on the quadrant in which the vector lies. In this example, the vector lies in the fourth quadrant, so the angle is measured counterclockwise from the positive x-axis. This means that the correct angle is 294.4439548 degrees, not 65.55604522 degrees. It is also important to consider the negative signs in the components of the vector, as they can affect the direction of the angle. In this case, the negative y-component (-7.70) indicates that the vector is pointing downwards, so the angle should be measured in the fourth quadrant. Therefore, the correct angle in this case is 294.4439548 degrees.