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Popular >

f(x)=(csc(x)-1)/(sin(x)-1)

Solution

f (x) = \frac{csc ( x ) - 1}{sin ( x ) - 1}

Solution

Period : 2 π

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

Range : f (x) < - 1 or f (x) \geq 1

Intercepts : None

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

Extreme Points : Minimum (\frac{3 π}{2} + 2 πn, 1)

+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, - 1) \cup [1, \infty)

Solution steps

Periodicity of

\frac{csc ( x ) - 1}{sin ( x ) - 1} : 2 π

Domain of

\frac{csc ( x ) - 1}{sin ( x ) - 1} : 2 πn < x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Range of

\frac{csc ( x ) - 1}{sin ( x ) - 1} : f (x) < - 1 or f (x) \geq 1

Axis interception points of

\frac{csc ( x ) - 1}{sin ( x ) - 1} :

None

Asymptotes of

\frac{csc ( x ) - 1}{sin ( x ) - 1} :

Vertical

: x = 2 πn, x = π + 2 πn

Extreme Points of

\frac{csc ( x ) - 1}{sin ( x ) - 1} :

Minimum

(\frac{3 π}{2} + 2 πn, 1)

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Frequently Asked Questions (FAQ)

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