I assume that 0 means theta in your post.
I will use x for 0 and then back-substitute at the end of the math work.
As you know, tan x = opposite/adjacent.
So, 3/4 = opposite side/adjacent side.
We are in quadrant 1. In quadrant 1 all trigonometric functions are positive.
We need to find the hypotenuse of the right triangle formed in quadrant 1 using the Pythagorean Theorem.
Do you remember the Pythagorean Theorem?
Here it is: a^2 + b^2 = h^2, where a = b = side of right triangle and h = hypotenuse.
Let a = 3
Let b = 4
We need to find h.
(3)^2 + (4)^2 = (h)^2
9 + 16 = (h)^2
25 = (h)^2
Taking the square root on both sides of the equation, we find h to be 5. All parts of the right triangle in quadrant 1 have been found.
You want to find cos x. What is cos x in terms of any right triangle? You know from class that cos x = adjacent side/hypotenuse.
Knowing this fact, cos x = 4/5.
Back-substitute for x.
Answer: cos (0) = 4/5.
I hope this helps.