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Popular >

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

Solution

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

Solution

Period : 2 π

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

Intercepts : None

Asymptotes : Vertical x = 2 πn, x = \frac{3 π}{2} + 2 πn, x = π + 2 πn

Extreme Points : Maximum (\frac{7 π}{6} + 2 πn, - 4), Maximum (\frac{11 π}{6} + 2 πn, - 4)

+1

Interval Notation

Domain : (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)

Solution steps

Periodicity of

\frac{csc ( x )}{1 + sin ( x )} : 2 π

Domain of

\frac{csc ( x )}{1 + sin ( x )} : 2 πn < x < π + 2 πn or π + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Axis interception points of

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

None

Asymptotes of

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

Vertical

: x = 2 πn, x = \frac{3 π}{2} + 2 πn, x = π + 2 πn

Extreme Points of

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

Maximum

(\frac{7 π}{6} + 2 πn, - 4),

Maximum

(\frac{11 π}{6} + 2 πn, - 4)

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Frequently Asked Questions (FAQ)

What is the f(x)=(csc(x))/(1+sin(x)) ?
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