a = (4, 4)^{T}
is oriented at 45°

Math should give the same answer:
The slope of **a** is

(change in y)/(change in x) = 4.0/4.0 = 1.0.

So the angle is `arc tan( 1.0 ) = 45°`

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Vectors have no location, so neither the length nor the direction depend on where you draw a vector. The formula for the direction of a 2D vector is

angle of (x, y)^{T}= arc tan( y/x )

Arc tan( z ) means "find the angle that has a tangent of z." When you do this with a calculator, remember that the answer may be in radians or in degrees. Most calculators give you the option of using use either format.

Also, since calculators usually give the answer as -90.0 to +90.0 degrees
(or -pi to +pi radians) *you may have to adjust the answer*.
More on this later.

You can use the calculator on your computer.
If you are using MS Windows, click "scientific" in the "view" menu for
a calculator that has arc tan.
Arc tan may be labeled `tan`

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^{-1}

What is the orientation of the vector represented by: **k** = (3,4)^{T} ?
(Do this with a calculator.)