Sec theta = 5/3 and the terminal point determined by quadrant 4

Here, we have

Since

So, for the angle θ,

Hypotenuse = 5 and Base = 3

Using Pythogoras theorem,

(Hypotenuse)² = (Base²) + (Perpendicular )²

(5 )² = ( 3 )² + (Perpendicular )²

⇒ Perpendicular = 25 - 9 = √16 = 4

we have given θ lie in IV quadrant. In IV quadrant cos and sec are positive function but sine, cosec, tan and cot are negative.

i would need to see the dot plot : )