What is the domain of (sin(x))/(cos(x)) ?

The domain of (sin(x))/(cos(x)) is pin<= x< pi/2+pin\lor pi/2+pin<x<pi+pin

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domain of (sin(x))/(cos(x))

domain

\frac{sin ( x )}{cos ( x )}

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

Interval Notation

Solution steps

Take the denominator(s) of

\frac{sin ( x )}{cos ( x )}

and compare to zero:

x = \frac{π}{2} + πn

Periodicity of

\frac{sin ( x )}{cos ( x )} : π

Combine period:

πn \leq x < π + πn

and undefined points.

The domain is

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

\frac{x ^{2} - 8 x + 15}{x + 12}

f (x) = \frac{ln ( x - 3 )}{x ^{2} - x - 2}

f (x) = \frac{7}{x + 4}

x 1 - x^{2}

\frac{1}{4 - 1 - x}

What is the domain of (sin(x))/(cos(x)) ?
The domain of (sin(x))/(cos(x)) is pin<= x< pi/2+pin\lor pi/2+pin<x<pi+pin