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Popular >

y= 1/4 csc(x+pi/4)

Solution

y = \frac{1}{4} csc (x + \frac{π}{4})

Solution

Period : 2 π

Domain : 2 πn \leq x < π - \frac{π}{4} + 2 πn or π - \frac{π}{4} + 2 πn < x < \frac{7 π}{4} + 2 πn or \frac{7 π}{4} + 2 πn < x < 2 π + 2 πn

Range : f (x) \leq - \frac{1}{4} or f (x) \geq \frac{1}{4}

Y Intercepts : (0, \frac{2}{4})

Asymptotes : Vertical x = \frac{7 π}{4} + 2 πn, x = π - \frac{π}{4} + 2 πn

Extreme Points : Minimum (\frac{π}{4} + 2 πn, \frac{1}{4}), Maximum (\frac{5 π}{4} + 2 πn, - \frac{1}{4})

+1

Interval Notation

Domain : [2 πn, π - \frac{π}{4} + 2 πn) \cup (π - \frac{π}{4} + 2 πn, \frac{7 π}{4} + 2 πn) \cup (\frac{7 π}{4} + 2 πn, 2 π + 2 πn)

Range : (- \infty, - \frac{1}{4}] \cup [\frac{1}{4}, \infty)

Solution steps

Periodicity of

\frac{1}{4} csc (x + \frac{π}{4}) : 2 π

Domain of

\frac{1}{4} csc (x + \frac{π}{4}) : 2 πn \leq x < π - \frac{π}{4} + 2 πn or π - \frac{π}{4} + 2 πn < x < \frac{7 π}{4} + 2 πn or \frac{7 π}{4} + 2 πn < x < 2 π + 2 πn

Range of

\frac{1}{4} csc (x + \frac{π}{4}) : f (x) \leq - \frac{1}{4} or f (x) \geq \frac{1}{4}

Axis interception points of

\frac{1}{4} csc (x + \frac{π}{4}) :

Y Intercepts

: (0, \frac{2}{4})

Asymptotes of

\frac{1}{4} csc (x + \frac{π}{4}) :

Vertical

: x = \frac{7 π}{4} + 2 πn, x = π - \frac{π}{4} + 2 πn

Extreme Points of

\frac{1}{4} csc (x + \frac{π}{4}) :

Minimum

(\frac{π}{4} + 2 πn, \frac{1}{4}),

Maximum

(\frac{5 π}{4} + 2 πn, - \frac{1}{4})

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Frequently Asked Questions (FAQ)

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