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Popular >

f(θ)=(sec(θ))/(1+sec(θ))

Solution

f (θ) = \frac{sec ( θ )}{1 + sec ( θ )}

Solution

Period : 2 π

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

Range : f (θ) \geq \frac{1}{2}

Y Intercepts : (0, \frac{1}{2})

Asymptotes : Vertical θ = π + 2 πn

Extreme Points : Minimum (2 πn, \frac{1}{2})

+1

Interval Notation

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

Range : [\frac{1}{2}, \infty)

Solution steps

Periodicity of

\frac{sec ( θ )}{1 + sec ( θ )} : 2 π

Domain of

\frac{sec ( θ )}{1 + sec ( θ )} : 2 πn \leq θ < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < θ < π + 2 πn or π + 2 πn < θ < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < θ < 2 π + 2 πn

Range of

\frac{sec ( θ )}{1 + sec ( θ )} : f (θ) \geq \frac{1}{2}

Axis interception points of

\frac{sec ( θ )}{1 + sec ( θ )} :

Y Intercepts

: (0, \frac{1}{2})

Asymptotes of

\frac{sec ( θ )}{1 + sec ( θ )} :

Vertical

: θ = π + 2 πn

Extreme Points of

\frac{sec ( θ )}{1 + sec ( θ )} :

Minimum

(2 πn, \frac{1}{2})

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Frequently Asked Questions (FAQ)

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