What is the domain of-2tan(θ+pi/4)-1 ?

The domain of-2tan(θ+pi/4)-1 is pin<= θ< pi/4+pin\lor pi/4+pin<θ<pi+pin

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domain of-2tan(θ+pi/4)-1

domain

- 2 tan (θ + \frac{π}{4}) - 1

πn \leq θ < \frac{π}{4} + πn or \frac{π}{4} + πn < θ < π + πn

Interval Notation

[πn, \frac{π}{4} + πn) \cup (\frac{π}{4} + πn, π + πn)

Solution steps

Take the denominator(s) of

- 2 tan (θ + \frac{π}{4}) - 1

and compare to zero:

θ = \frac{π}{4} + πn

Periodicity of

- 2 tan (θ + \frac{π}{4}) - 1 : π

Combine period:

πn \leq θ < π + πn

and undefined points.

The domain is

πn \leq θ < \frac{π}{4} + πn or \frac{π}{4} + πn < θ < π + πn

What is the domain of-2tan(θ+pi/4)-1 ?
The domain of-2tan(θ+pi/4)-1 is pin<= θ< pi/4+pin\lor pi/4+pin<θ<pi+pin