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Popular >

y=3csc(x/3)

Solution

y = 3 csc (\frac{x}{3})

Solution

Period : 6 π

Domain : 6 πn < x < 3 π + 6 πn or 3 π + 6 πn < x < 6 π + 6 πn

Range : f (x) \leq - 3 or f (x) \geq 3

Intercepts : None

Asymptotes : Vertical x = 3 π + 6 πn, x = 6 πn

Extreme Points : Minimum (\frac{3 π}{2} + 6 πn, 3), Maximum (\frac{9 π}{2} + 6 πn, - 3)

+1

Solution steps

Periodicity of

3 csc (\frac{x}{3}) : 6 π

Domain of

3 csc (\frac{x}{3}) : 6 πn < x < 3 π + 6 πn or 3 π + 6 πn < x < 6 π + 6 πn

Range of

3 csc (\frac{x}{3}) : f (x) \leq - 3 or f (x) \geq 3

Axis interception points of

3 csc (\frac{x}{3}) :

None

Asymptotes of

3 csc (\frac{x}{3}) :

Vertical

: x = 3 π + 6 πn, x = 6 πn

Extreme Points of

3 csc (\frac{x}{3}) :

Minimum

(\frac{3 π}{2} + 6 πn, 3),

Maximum

(\frac{9 π}{2} + 6 πn, - 3)

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