What is the domain of sec(θ) ?

The domain of sec(θ) is 2pin<= θ< pi/2+2pin\lor pi/2+2pin<θ<(3pi)/2+2pin\lor (3pi)/2+2pin<θ<2pi+2pin

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domain of sec(θ)

domain

2 πn \leq θ < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < θ < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < θ < 2 π + 2 πn

Interval Notation

[2 πn, \frac{π}{2} + 2 πn) \cup (\frac{π}{2} + 2 πn, \frac{3 π}{2} + 2 πn) \cup (\frac{3 π}{2} + 2 πn, 2 π + 2 πn)

Solution steps

Take the denominator(s) of

sec (θ)

and compare to zero:

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

Periodicity of

sec (θ) : 2 π

Combine period:

2 πn \leq θ < 2 π + 2 πn

and undefined points.

The domain is

2 πn \leq θ < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < θ < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < θ < 2 π + 2 πn

What is the domain of sec(θ) ?
The domain of sec(θ) is 2pin<= θ< pi/2+2pin\lor pi/2+2pin<θ<(3pi)/2+2pin\lor (3pi)/2+2pin<θ<2pi+2pin