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Popular >

f(x)=cot^2(x)+csc(x)-11

Solution

f (x) = cot^{2} (x) + csc (x) - 11

Solution

Period : 2 π

Domain : 2 πn < x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Range : f (x) \geq - 12

X Intercepts : (arccsc (3) + 2 πn, 0), (π - arccsc (3) + 2 πn, 0), (- arccsc (4) + 2 π + 2 πn, 0), (π + arccsc (4) + 2 πn, 0)

Asymptotes : Vertical x = 2 πn, x = π + 2 πn

Extreme Points : Minimum (\frac{π}{2} + 2 πn, - 10), Minimum (\frac{3 π}{2} + 2 πn, - 12)

+1

Interval Notation

Domain : (2 πn, π + 2 πn) \cup (π + 2 πn, 2 π + 2 πn)

Range : [- 12, \infty)

Solution steps

Periodicity of

cot^{2} (x) + csc (x) - 11 : 2 π

Domain of

cot^{2} (x) + csc (x) - 11 : 2 πn < x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Range of

cot^{2} (x) + csc (x) - 11 : f (x) \geq - 12

Axis interception points of

cot^{2} (x) + csc (x) - 11 :

X Intercepts

: (arccsc (3) + 2 πn, 0), (π - arccsc (3) + 2 πn, 0), (- arccsc (4) + 2 π + 2 πn, 0), (π + arccsc (4) + 2 πn, 0)

Asymptotes of

cot^{2} (x) + csc (x) - 11 :

Vertical

: x = 2 πn, x = π + 2 πn

Extreme Points of

cot^{2} (x) + csc (x) - 11 :

Minimum

(\frac{π}{2} + 2 πn, - 10),

Minimum

(\frac{3 π}{2} + 2 πn, - 12)

Popular Examples

f (x) = (1 + x)^{n}

y = - 2 x^{2} - 3 x - 5

y=-10x^2+60x+10

y = - 10 x^{2} + 60 x + 10

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f (x) = 4 x^{3} e^{- x}

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Frequently Asked Questions (FAQ)

What is the f(x)=cot^2(x)+csc(x)-11 ?
The f(x)=cot^2(x)+csc(x)-11 is