can cosecant equal zero
Asymptotes of Secant, Cosecant, and Cotangent. To find the x-intercepts and asymptotes of secant, cosecant, and cotangent, rewrite them in terms of sine and cosine. Notice that since secant and cosecant have 1 in the numerator and a trig function in the denominator, they can never equal zero; they do not have x-intercepts. The vertical asymptotes of the three functions are whenever the denominators are zero.