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Popular >

f(θ)=2sec^2(θ/2)

Solution

f (θ) = 2 sec^{2} (\frac{θ}{2})

Solution

Period : 2 π

Domain : 2 πn \leq θ < π + 2 πn or π + 2 πn < θ < 2 π + 2 πn

Range : f (θ) \geq 2

Y Intercepts : (0, 2)

Asymptotes : Vertical θ = π + 2 πn

Extreme Points : Minimum (2 πn, 2)

+1

Interval Notation

Domain : [2 πn, π + 2 πn) \cup (π + 2 πn, 2 π + 2 πn)

Range : [2, \infty)

Solution steps

Periodicity of

2 sec^{2} (\frac{θ}{2}) : 2 π

Domain of

2 sec^{2} (\frac{θ}{2}) : 2 πn \leq θ < π + 2 πn or π + 2 πn < θ < 2 π + 2 πn

Range of

2 sec^{2} (\frac{θ}{2}) : f (θ) \geq 2

Axis interception points of

2 sec^{2} (\frac{θ}{2}) :

Y Intercepts

: (0, 2)

Asymptotes of

2 sec^{2} (\frac{θ}{2}) :

Vertical

: θ = π + 2 πn

Extreme Points of

2 sec^{2} (\frac{θ}{2}) :

Minimum

(2 πn, 2)

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