x-axis component = the magnitude of the vector multiplied by sin 30
Bx = 15 sin 30
y-axis component = the magnitude of the vector multiplied by cos 30
By = 15 cos 30
***pay attention to whether the given angle is opposite or adjacent, because this will also give the equivalent answer:***
Bx = 15 cos 60
By = 15 sin 60
I generally always calculate the angle from the positive x-axis and use that, because I know that the cosine of that angle will always give me the x component of the vector without possibly making mistakes in whether to use sine or cosine, and it will also automatically give me the correct sign for the vector component.
x-axis component of vector B = 7.5
y-axis component of vector B = 13
I'm going to give an example of adding 2 random vectors, when you figure out the components of each vector it's easy to use this formula. Basically you add the x-components of each vector together and that sum is the x-component of the resultant vector, and same for the y-components. The formula is this:
So for example if we had 2 vectors <2, 1> and <-4, 3> the sum of those two vectors would be <-2, 4>
Subtraction is the same process:
To find the direction of a vector take the inverse tangent of the y-component divided by the x-component, or arctan (y/x). The magnitude of any vector