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Popular >

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

Solution

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

Solution

Period : 2 π

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

Range : - 1 < f (y) \leq 1

Intercepts : None

Asymptotes : None

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

+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)

Range : (- 1, 1]

Solution steps

Periodicity of

\frac{1 + sin ( y )}{1 + csc ( y )} : 2 π

Domain of

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

Range of

\frac{1 + sin ( y )}{1 + csc ( y )} : - 1 < f (y) \leq 1

Axis interception points of

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

None

Asymptotes of

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

None

Extreme Points of

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

Maximum

(\frac{π}{2} + 2 πn, 1)

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Frequently Asked Questions (FAQ)

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