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.