You probably know that the cotangent of an angle is the reciprocal of the tangent of the same angle.
So you already know that the tangent of this angle is 12/5. This is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. You can go ahead and draw a right triangle with opposite side of length 12 and adjacent side of length 5, since all right triangles with that ratio of lengths will have the same trigonometric properties.
From the Pythagorean theorem, you can find the length of the hypotenuse, which allows you to find the sine and cosine of this angle.