How do I find the direction angle of vector #<-2, -5>#?
1 Answer
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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.
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.
![Vector Vector](https://answers.unity.com/storage/temp/3467-angle-vectors.jpg)
![Vector Vector](https://www.wikihow.com/images/thumb/e/e0/Find-the-Magnitude-of-a-Vector-Step-1-Version-3.jpg/v4-460px-Find-the-Magnitude-of-a-Vector-Step-1-Version-3.jpg.webp)
Step 2-
Draw your vector!
#<-2,-5># or #-2i-5j# 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).
Draw your vector!
Step 3-
Figure out the angle your vector makes with the x-axis, using some trig.
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.
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:
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The direction angle for #<-2,-5># , measured counterclockwise from the positive #x# axis, is #248.2°#