Graphing parameters of. y = sec(x) and y = csc (x)

range: (-∞ , -1) ∪ (1 , ∞)
Period = 2π
Horizontal Shift (translation) = d , to the left if (- d) is positive and to the right if (- d) is negative.
Vertical asymptotes of y = sec(x) = 1 / cos(x) at the zeros of cos(x) given by x = π/2 kπ , k = 0 , ~ mn~1, ~ mn~2, …
Vertical asymptotes of y = csc(x) = 1 / sin(x) at the zeros of sin(x) given by x = kπ , k = 0 , ~ mn~1, ~ mn~2, …
We need to know how to sketch basic secant and cosecant functions using the identities y = sec(x) = 1 / cos(x) and y = csc(x) = 1 / sin(x) to understand the vertical asymptotes.