Question

A vector points -43.0 unitsalong the x-axis, and 11.1 unitsalong the y-axis.Find the direction of the vector.Y

Answer 1

The vector will be represent (not accurately) like the diagram below:

Now, from the expression

$\theta=\tan ^{-1}(\frac{v_x}{v_y})$

we get the pink angle, but we need the green angle. To get the correct one we calculate the pink one and then we find its supplementary angle; let's do that:

$\begin{gathered} \theta=\tan ^{-1}(\frac{11.1}{43}) \\ \theta=14.47 \end{gathered}$

Now, the green angle will be:

$180-14.47=165.53$

Therefore the direction of the vector is 165.53°