If tan0= 3/4, find cos0

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.

cos (0) = 4/5.

I hope this helps.

expression #3 is not equivalent. the others are.