What is the domain of $f (x) = sec x$ $f(x)=secx$ ?

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Answer 1 · 2014-10-17T18:22:03

By rewriting a bit,

$f (x) = sec x = \frac{1}{cos x}$ $f(x)=secx=1/cosx$ .

Since the denominator cannot be zero, we need to exclude numbers that make $cos x$ $cosx$ equal to zero.

Since for all integer $n$ $n$ ,

$cos (\frac{π}{2} + n π) = cos (\frac{2 n + 1}{2} π) = 0$ $cos(pi/2+npi)=cos({2n+1}/2pi)=0$ ,

the domain of $f$ $f$ is all real numbers except for $x = \frac{2 n + 1}{2} π$ $x={2n+1}/2pi$ for all integer $n$ $n$ .

I hope that this was helpful.

What is the domain of f(x)=secxf(x)=secx?