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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 : π

Domain : πn \leq x < 1 + πn or 1 + πn < x < π + πn

Range : f (x) \geq 1

Y Intercepts : (0, \frac{csc ( 0 - 1 )}{sin ( 0 - 1 )})

Asymptotes : Vertical x = 1 + πn

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

+1

Interval Notation

Domain : [πn, 1 + πn) \cup (1 + πn, π + πn)

Range : [1, \infty)

Solution steps

Periodicity of

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

Domain of

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

Range of

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

Axis interception points of

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

Y Intercepts

: (0, \frac{csc ( 0 - 1 )}{sin ( 0 - 1 )})

Asymptotes of

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

Vertical

: x = 1 + πn

Extreme Points of

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

Minimum

(\frac{π}{2} + 1 + πn, 1)

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Frequently Asked Questions (FAQ)

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