What would cos\theta be if angle theta passes (-4, 3)?

Trigonometry is based on a picture of a circle with the radius making an angle with the x axis. You carry this picture in your head, not your calculator. Trig is mostly imagination and the rest memorization.

Remember Chief SohCahToa
Sin = Opposite/Hypotenuse
Cosine = Adjacent/Hypotenuse
Tangent = Opposite/Adjacent

Also memorize:
Sec = 1/Cos
Csc = 1/Sin
Cot = 1/Tan

The radius is 1 unless otherwise specified. Getting to (-4, 3) makes the angle greater than 90 degrees. The opposite side is the vertical and that is 3. The adjacent side is horizontal and that is -4. So the cosine of the angle is -4/3.

BTW the radius in this case is not 1, it is 5.