Question

Where are the vertical asymptotes on the graph of the secant function?

Answer 1

Answer:

x=pi/2+n pi

Step-by-step explanation:

Answer 2

Using asymptote concepts, it is found that the vertical asymptotes on the graph of the secant function are:

$x = \frac{k\pi}{2}, k = \pm 1, \pm 3, \pm 5, ...$

• The vertical asymptotes of a function are the values of x which are outside the function domain.

• The secant function is:

$\sec{x} = \frac{1}{\cos{x}}$

• The vertical asymptotes are when the denominator is 0, thus, the values of x for which:

$\cos{x} = 0$

The solution is:

$x = \frac{k\pi}{2}, k = \pm 1, \pm 3, \pm 5, ...$

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