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Popular Functions >

y=tan(3x)csc(3x)

Solution

y = tan (3 x) csc (3 x)

Solution

Period : \frac{2 π}{3}

Domain : \frac{2 π}{3} n < x < \frac{π}{6} + \frac{2 π}{3} n or \frac{π}{6} + \frac{2 π}{3} n < x < \frac{π}{3} + \frac{2 π}{3} n or \frac{π}{3} + \frac{2 π}{3} n < x < \frac{π}{2} + \frac{2 π}{3} n or \frac{π}{2} + \frac{2 π}{3} n < x < \frac{2 π}{3} + \frac{2 π}{3} n

Range : f (x) < - 1 or f (x) > 1

Intercepts : None

Asymptotes : Vertical x = \frac{π}{2} + \frac{2 π}{3} n, x = \frac{π}{6} + \frac{2 π}{3} n

Extreme Points : None

+1

Interval Notation

Domain : (\frac{2 π}{3} n, \frac{π}{6} + \frac{2 π}{3} n) \cup (\frac{π}{6} + \frac{2 π}{3} n, \frac{π}{3} + \frac{2 π}{3} n) \cup (\frac{π}{3} + \frac{2 π}{3} n, \frac{π}{2} + \frac{2 π}{3} n) \cup (\frac{π}{2} + \frac{2 π}{3} n, \frac{2 π}{3} + \frac{2 π}{3} n)

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

Solution steps

Periodicity of

tan (3 x) csc (3 x) : \frac{2 π}{3}

Domain of

tan (3 x) csc (3 x) : \frac{2 π}{3} n < x < \frac{π}{6} + \frac{2 π}{3} n or \frac{π}{6} + \frac{2 π}{3} n < x < \frac{π}{3} + \frac{2 π}{3} n or \frac{π}{3} + \frac{2 π}{3} n < x < \frac{π}{2} + \frac{2 π}{3} n or \frac{π}{2} + \frac{2 π}{3} n < x < \frac{2 π}{3} + \frac{2 π}{3} n

Range of

tan (3 x) csc (3 x) : f (x) < - 1 or f (x) > 1

Axis interception points of

tan (3 x) csc (3 x) :

None

Asymptotes of

tan (3 x) csc (3 x) :

Vertical

: x = \frac{π}{2} + \frac{2 π}{3} n, x = \frac{π}{6} + \frac{2 π}{3} n

Extreme Points of

tan (3 x) csc (3 x) :

None

Graph

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Frequently Asked Questions (FAQ)

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