Find the direction of A= <-5,12>
I did arctan (12/-5) and added 180 because x was negative and got 105.13 degrees.
I missed the question on the test though. What did I do wrong?
180+arctan(12/-5) = 112.6
Are you talking about the direction of the angle A from the origin to (-5,12) ?
I have never seen that notation before.
I agree with FredR's answer, if I interpreted the question correctly.
It could be interpreted as the azimuth, which in surveying applications is typically measured in a clockwise direction from north.
To find the direction of a vector, you can use the trigonometric function arctan (also known as the inverse tangent). However, there is an issue in how you approached the problem.
When using arctan, the typical notation is arctan(y/x), where y refers to the vertical component and x refers to the horizontal component. In your case, you used arctan(12/-5). This implies that the y-component is 12, and the x-component is -5, but that is incorrect.
You need to use the x-component as the denominator and the y-component as the numerator. So in your case, the correct calculation should be arctan(-5/12). This will give you the angle in radians.
Additionally, since your x-component (-5) is negative, you should add 180 degrees (or π radians) to the result of arctan to correct for the quadrant in which the vector lies. This step ensures that the direction angle is measured counterclockwise from the positive x-axis.
So, the correct calculation should be:
Angle = arctan(-5/12) + 180
By using the correct calculation, you should get the correct direction of the vector A.