and tangent is the ratio of opposite/adjacent, OPP/ADJ, consider a triangle with theta and sides 3 and 4. The hypotenuse must be 5. You can calculate it or if you know, it is the pythagorean triple 3, 4, 5. See image.
Cosecant is the reciprocal of sine. Sin(theta) = 3/5
We are given with arc AC = 130 The measure of the arc on the other side of the circle is 360 - 130 = 230 Therefore, according to the theorem on circles, the measure of angle ABC is (1/2) ( 230 - 130) = 50