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Popular >

f(θ)=2csc(2θ)

Solution

f (θ) = 2 csc (2 θ)

Solution

Period : π

Domain : πn < θ < \frac{π}{2} + πn or \frac{π}{2} + πn < θ < π + πn

Range : f (θ) \leq - 2 or f (θ) \geq 2

Intercepts : None

Asymptotes : Vertical θ = \frac{π}{2} + πn, θ = πn

Extreme Points : Minimum (\frac{π}{4} + πn, 2), Maximum (\frac{3 π}{4} + πn, - 2)

+1

Interval Notation

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

Range : (- \infty, - 2] \cup [2, \infty)

Solution steps

Periodicity of

2 csc (2 θ) : π

Domain of

2 csc (2 θ) : πn < θ < \frac{π}{2} + πn or \frac{π}{2} + πn < θ < π + πn

Range of

2 csc (2 θ) : f (θ) \leq - 2 or f (θ) \geq 2

Axis interception points of

2 csc (2 θ) :

None

Asymptotes of

2 csc (2 θ) :

Vertical

: θ = \frac{π}{2} + πn, θ = πn

Extreme Points of

2 csc (2 θ) :

Minimum

(\frac{π}{4} + πn, 2),

Maximum

(\frac{3 π}{4} + πn, - 2)

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