Components, Magnitude and Angle of a vector.

By positioning the point A, the values for the Vector from the origin to point A are shown. Both the components and ,magnitude and angle, are shown as well as the equations for translating between values.
Try moving the point to the various quadrants. Look at the signs of the components. Imagine a reference triangle between the vector and the x axis, what would sine and cosine of the origin angle be relative to the component signs?