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Popular >

y=csc(x-pi/4)

Solution

y = csc (x - \frac{π}{4})

Solution

Period : 2 π

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

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

Y Intercepts : (0, - 2)

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

Extreme Points : Minimum (\frac{3 π}{4} + 2 πn, 1), Maximum (\frac{7 π}{4} + 2 πn, - 1)

+1

Interval Notation

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

Range : (- \infty, - 1] \cup [1, \infty)

Solution steps

Periodicity of

csc (x - \frac{π}{4}) : 2 π

Domain of

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

Range of

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

Axis interception points of

csc (x - \frac{π}{4}) :

Y Intercepts

: (0, - 2)

Asymptotes of

csc (x - \frac{π}{4}) :

Vertical

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

Extreme Points of

csc (x - \frac{π}{4}) :

Minimum

(\frac{3 π}{4} + 2 πn, 1),

Maximum

(\frac{7 π}{4} + 2 πn, - 1)

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Frequently Asked Questions (FAQ)

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