Tangent is defined as the length of the opposite side of the triangle divided by the length of the adjacent side of the triangle. Since you know that two of the legs are 3 and 4, using the pythagorean theorem you know that the last side is 5. Sin is defined as the length of the opposite side divided by the length of the hypotenuse, which in this case is 3/5. Cosecant is just the reciprocal of that, or 5/3. Hope this helps!
