Question

Find sec Θ if the terminal side of Θ in standard position contains the point (4, -3)

Answer 1

If we plot that point we find ourselves in QIV.  The distance along the x axis is 4, and the distance down from that point is -3.  If we create a right triangle with that segment, that segment serves as the hypotenuse of the triangle.  We need its measure.  Using Pythagorean's theorem, $4^2+-3^2=c^2$ and $16+9=c^2$.  We see that c = 5.  We need now to find the secant of that right triangle.  Secant if the co-identity of cosine which is side adjacent over hypotenuse.  That means that secant is the hypotenuse over the side adjacent.  So our secant theta = 5/4

Answer 2

Sec Θ = hyp/adj

If we draw a right triangle in quadrant 4, we learn that the hypotenuse is 5.

In quadrant 4, secant is positive.

sec Θ = 5/4 = answer