Question

find remaining functions sec(x)=5/4, tan(x) < 0

Answer 1

Before we do anything else you can find the value of cos(x)

Answer 2

This helps with the cosine.
\(\sec x = \dfrac{1}{\cos x} \)

Answer 3

Now if cosine is positive and tangent is negative, then sine has what sign?

Answer 4

Also, \(\tan x \lt 0\) limits the angle to two quadrants.