# How do I find the direction angle of vector <-2, -5>?

Mar 13, 2015

Step 1-
Decide from where you are going to measure your angle. Let's go with the convention: measuring a positive angle going counterclockwise from the positive x-axis.

Step 2-
$< - 2 , - 5 >$ or $- 2 i - 5 j$ is in the third quadrant. You go $2$ units to the left on the $x$ axis (in the negative $i$ direction), and then from there down $5$ units on the y axis (so below the origin).

Step 3-
Figure out the angle your vector makes with the x-axis, using some trig.

Step 4-
Figure out the overall angle starting from the positive x-axis from your sketch.

Now, you could actually have an infinite amount of solutions depending on where you are measuring your angle from (or you could just keep adding 360°  to get to the same place).

For example, another valid solution is to say that your direction angle, measured clockwise from the positive $x$ axis is 360° - 248.2°= 141.6°. Just make sure you specify what your frame of reference is.

For this case, I'm going to say the final answer is:

The direction angle for $< - 2 , - 5 >$, measured counterclockwise from the positive $x$ axis, is 248.2°