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Popular Functions >

f(θ)= 4/(2sin(θ)-1)

Solution

f (θ) = \frac{4}{2 sin ( θ ) - 1}

Solution

Period : 2 π

Domain : 2 πn \leq θ < \frac{π}{6} + 2 πn or \frac{π}{6} + 2 πn < θ < \frac{5 π}{6} + 2 πn or \frac{5 π}{6} + 2 πn < θ < 2 π + 2 πn

Range : f (θ) \leq - \frac{4}{3} or f (θ) \geq 4

Y Intercepts : (0, - 4)

Asymptotes : Vertical θ = \frac{5 π}{6} + 2 πn, θ = \frac{π}{6} + 2 πn

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

+1

Interval Notation

Domain : [2 πn, \frac{π}{6} + 2 πn) \cup (\frac{π}{6} + 2 πn, \frac{5 π}{6} + 2 πn) \cup (\frac{5 π}{6} + 2 πn, 2 π + 2 πn)

Range : (- \infty, - \frac{4}{3}] \cup [4, \infty)

Solution steps

Periodicity of

\frac{4}{2 sin ( θ ) - 1} : 2 π

Domain of

\frac{4}{2 sin ( θ ) - 1} : 2 πn \leq θ < \frac{π}{6} + 2 πn or \frac{π}{6} + 2 πn < θ < \frac{5 π}{6} + 2 πn or \frac{5 π}{6} + 2 πn < θ < 2 π + 2 πn

Range of

\frac{4}{2 sin ( θ ) - 1} : f (θ) \leq - \frac{4}{3} or f (θ) \geq 4

Axis interception points of

\frac{4}{2 sin ( θ ) - 1} :

Y Intercepts

: (0, - 4)

Asymptotes of

\frac{4}{2 sin ( θ ) - 1} :

Vertical

: θ = \frac{5 π}{6} + 2 πn, θ = \frac{π}{6} + 2 πn

Extreme Points of

\frac{4}{2 sin ( θ ) - 1} :

Minimum

(\frac{π}{2} + 2 πn, 4),

Maximum

(\frac{3 π}{2} + 2 πn, - \frac{4}{3})

Graph

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Frequently Asked Questions (FAQ)

What is the f(θ)= 4/(2sin(θ)-1) ?
The f(θ)= 4/(2sin(θ)-1) is