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Popular >

f(θ)=(cot^2(θ))/(csc(θ)-1)

Solution

f (θ) = \frac{cot ^{2} ( θ )}{csc ( θ ) - 1}

Solution

Period : 2 π

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

Range : f (θ) \leq 0 or f (θ) > 2

X Intercepts : (\frac{π}{2} + 2 πn, 0), (\frac{3 π}{2} + 2 πn, 0)

Asymptotes : Vertical θ = 2 πn, θ = π + 2 πn

Extreme Points : Maximum (\frac{3 π}{2} + 2 πn, 0)

+1

Interval Notation

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

Range : (- \infty, 0] \cup (2, \infty)

Solution steps

Periodicity of

\frac{cot ^{2} ( θ )}{csc ( θ ) - 1} : 2 π

Domain of

\frac{cot ^{2} ( θ )}{csc ( θ ) - 1} : 2 πn < θ < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < θ < π + 2 πn or π + 2 πn < θ < 2 π + 2 πn

Range of

\frac{cot ^{2} ( θ )}{csc ( θ ) - 1} : f (θ) \leq 0 or f (θ) > 2

Axis interception points of

\frac{cot ^{2} ( θ )}{csc ( θ ) - 1} :

X Intercepts

: (\frac{π}{2} + 2 πn, 0), (\frac{3 π}{2} + 2 πn, 0)

Asymptotes of

\frac{cot ^{2} ( θ )}{csc ( θ ) - 1} :

Vertical

: θ = 2 πn, θ = π + 2 πn

Extreme Points of

\frac{cot ^{2} ( θ )}{csc ( θ ) - 1} :

Maximum

(\frac{3 π}{2} + 2 πn, 0)

Popular Examples

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Frequently Asked Questions (FAQ)

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