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Popular >

f(θ)=sin(θ)tan(θ)csc^2(θ)

Solution

f (θ) = sin (θ) tan (θ) csc^{2} (θ)

Solution

Period : 2 π

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

Range : f (θ) < - 1 or f (θ) > 1

Intercepts : None

Asymptotes : Vertical θ = \frac{3 π}{2} + 2 πn, θ = \frac{π}{2} + 2 πn

Extreme Points : None

+1

Interval Notation

Domain : (2 πn, \frac{π}{2} + 2 πn) \cup (\frac{π}{2} + 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 : (- \infty, - 1) \cup (1, \infty)

Solution steps

Periodicity of

sin (θ) tan (θ) csc^{2} (θ) : 2 π

Domain of

sin (θ) tan (θ) csc^{2} (θ) : 2 πn < θ < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < θ < π + 2 πn or π + 2 πn < θ < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < θ < 2 π + 2 πn

Range of

sin (θ) tan (θ) csc^{2} (θ) : f (θ) < - 1 or f (θ) > 1

Axis interception points of

sin (θ) tan (θ) csc^{2} (θ) :

None

Asymptotes of

sin (θ) tan (θ) csc^{2} (θ) :

Vertical

: θ = \frac{3 π}{2} + 2 πn, θ = \frac{π}{2} + 2 πn

Extreme Points of

sin (θ) tan (θ) csc^{2} (θ) :

None

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Frequently Asked Questions (FAQ)

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