Asymptotes of Secant, Cosecant, and Cotangent - Concept

Concept Concept (1)

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.

Sample Sample Problems (3)

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Asymptotes of Secant, Cosecant, and Cotangent - Problem 1
Problem 1
How to find the x-intercepts and vertical asymptotes of y = 5 sec(x/6).
Asymptotes of Secant, Cosecant, and Cotangent - Problem 2
Problem 2
How to find the x-intercepts and vertical asymptotes of y = (-1/4) csc(pix/6 + pi/3).
Asymptotes of Secant, Cosecant, and Cotangent - Problem 3
Problem 3
How to find the x-intercepts and vertical asymptotes of y = cot(pi x square root x/2).