Let cos(theta)= 4/5, where theta is an angle in qiv. find the sine, tangent, cotangent, cosecant, and secant of theta

Cosine is adjacent/hypotenuse.
Draw a right triangle and you can see that the hypotenuse is 5, one of the legs is 4, and the missing leg would be 3 (3,4,5 Pythagorean triangle).

Now that you have all the sides, use the same angle to find all the other trig functions.
sine = opposite/hypotenuse = 3/5
cotangent = adjacent/opposite = 4/3
cosecant = hypotenuse/opposite = 5/3
secant = hypotenuse/adjacent = 5/4