Sketch Trigonometric Functions  secant and cosecant
The sketching of the secant and cosecant functions of the form y = a sec( k ( x  d)) and y = a csc( k ( x  d)) are discussed with detailed examples.
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.
y = sec(x) = 1 / cos(x)
All zeros of cos(x) (which is in the denominator) are vertical asymptotes of the sec(x).
y = csc(x) = 1 / sin(x)
All zeros of sin(x) (which is in the denominator) are vertical asymptotes of the csc(x).

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