If tan (theta) = 5/4 and cos (theta) < 0, find the other trig. functions.

Base on your question where tan(theta) = 5/4 and cos(theta) is less than 0 i think the remaining trigonometric function values are the following:
sin = (-5*sqrt of 41)/41, csc=sqrt of 41/5, sec = -sqrt of 41/5 and cot is 4/5.
I hope you understand my answer and able to answer your questions.

The answer would be (c)