Determine the direction angle (in degrees) for each vector:

Question

Make sure you’re using degrees instead of radians.
If you use a decimal approximation, you must be accurate to at least 3 decimal places.

⟨6,−5⟩ has direction angle: θ= 140.194 but it says im wrong.

What I did is tan^-1(-5/6)= -39.80557109

I then add 180 to -39.80557109 and i got 140.194.

Answer 1

Sketch ⟨6,−5⟩ and it will be in the fourth quadrant

angle in standard position is tan^-1 (5/6) = 39.816°

so in quad IV it would be 360-39.81 = 320.194°
notice this would be coterminal with your angle of -39.816°

Are you not familiar with the CAST rule?

Answer 2

Tan A = -5/6
A = -39.806o = 39.806o S. of E. = 320.194o CCW from +x-axis.