Final answer:
The csc, sec, and cot graphs have asymptotes where their corresponding sine, cosine, and tangent functions are zero, which is at integer multiples of π for csc and cot, and odd multiples of π/2 for sec.
Step-by-step explanation:
The asymptotes of the cosecant (csc), secant (sec), and cotangent (cot) graphs occur where their respective reciprocal trigonometric functions sine, cosine, and tangent equal zero, as they approach infinity or negative infinity at these points.
For the cosecant graph, which is the reciprocal of the sine function, asymptotes occur at integer multiples of π, since sine is zero at these points. The secant graph has asymptotes where cosine equals zero, which is at odd multiples of π/2 (or π(1/2 + n), where n is an integer). Lastly, the cotangent graph, being the reciprocal of the tangent function, has its asymptotes at the integer multiples of π, which are the points where the tangent function is zero.