What is the domain of f(x)= 1/(tan(x)) ?

The domain of f(x)= 1/(tan(x)) is pin<x< pi/2+pin\lor pi/2+pin<x<pi+pin

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domain of f(x)= 1/(tan(x))

domain

f (x) = \frac{1}{tan ( x )}

πn < x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

Interval Notation

(πn, \frac{π}{2} + πn) \cup (\frac{π}{2} + πn, π + πn)

Solution steps

Take the denominator(s) of

\frac{1}{tan ( x )}

and compare to zero:

x = πn, x = \frac{π}{2} + πn

Periodicity of

\frac{1}{tan ( x )} : π

Combine period:

πn \leq x < π + πn

and undefined points.

The domain is

πn < x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

y = 5 x - 5

+ 4 x + 20

g (x) = 3^{x - 2}

f (x) = \frac{2}{3} x^{2} + 1^{3}

f (x) = \frac{- 3}{5 x + 20} + 7

What is the domain of f(x)= 1/(tan(x)) ?
The domain of f(x)= 1/(tan(x)) is pin<x< pi/2+pin\lor pi/2+pin<x<pi+pin