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