What is the domain of y=tan(t) ?

The domain of y=tan(t) is pin<= t< pi/2+pin\lor pi/2+pin<t<pi+pin

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domain of y=tan(t)

domain

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

Interval Notation

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

Solution steps

Take the denominator(s) of

tan (t)

and compare to zero:

t = \frac{π}{2} + πn

Periodicity of

tan (t) : π

Combine period:

πn \leq t < π + πn

and undefined points.

The domain is

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

What is the domain of y=tan(t) ?
The domain of y=tan(t) is pin<= t< pi/2+pin\lor pi/2+pin<t<pi+pin