Question

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

-3/4

-5/3

5/4

4/5

Answer 1

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

Answer 2

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