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Popular >

f(x)=cot^2(x)+csc(x)-1

Solution

f (x) = cot^{2} (x) + csc (x) - 1

Solution

Period : 2 π

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

Range : f (x) \geq - 2

X Intercepts : (\frac{π}{2} + 2 πn, 0), (\frac{7 π}{6} + 2 πn, 0), (\frac{11 π}{6} + 2 πn, 0)

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

Extreme Points : Minimum (\frac{π}{2} + 2 πn, 0), Minimum (\frac{3 π}{2} + 2 πn, - 2)

+1

Interval Notation

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

Range : [- 2, \infty)

Solution steps

Periodicity of

cot^{2} (x) + csc (x) - 1 : 2 π

Domain of

cot^{2} (x) + csc (x) - 1 : 2 πn < x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Range of

cot^{2} (x) + csc (x) - 1 : f (x) \geq - 2

Axis interception points of

cot^{2} (x) + csc (x) - 1 :

X Intercepts

: (\frac{π}{2} + 2 πn, 0), (\frac{7 π}{6} + 2 πn, 0), (\frac{11 π}{6} + 2 πn, 0)

Asymptotes of

cot^{2} (x) + csc (x) - 1 :

Vertical

: x = 2 πn, x = π + 2 πn

Extreme Points of

cot^{2} (x) + csc (x) - 1 :

Minimum

(\frac{π}{2} + 2 πn, 0),

Minimum

(\frac{3 π}{2} + 2 πn, - 2)

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Frequently Asked Questions (FAQ)

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