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Popular >

f(x)=cot^2(x)+csc(x)-5

Solution

f (x) = cot^{2} (x) + csc (x) - 5

Solution

Period : 2 π

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

Range : f (x) \geq - 6

X Intercepts : (\frac{π}{6} + 2 πn, 0), (\frac{5 π}{6} + 2 πn, 0), (- arccsc (3) + 2 π + 2 πn, 0), (π + arccsc (3) + 2 πn, 0)

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

Extreme Points : Minimum (\frac{π}{2} + 2 πn, - 4), Minimum (\frac{3 π}{2} + 2 πn, - 6)

+1

Interval Notation

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

Range : [- 6, \infty)

Solution steps

Periodicity of

cot^{2} (x) + csc (x) - 5 : 2 π

Domain of

cot^{2} (x) + csc (x) - 5 : 2 πn < x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Range of

cot^{2} (x) + csc (x) - 5 : f (x) \geq - 6

Axis interception points of

cot^{2} (x) + csc (x) - 5 :

X Intercepts

: (\frac{π}{6} + 2 πn, 0), (\frac{5 π}{6} + 2 πn, 0), (- arccsc (3) + 2 π + 2 πn, 0), (π + arccsc (3) + 2 πn, 0)

Asymptotes of

cot^{2} (x) + csc (x) - 5 :

Vertical

: x = 2 πn, x = π + 2 πn

Extreme Points of

cot^{2} (x) + csc (x) - 5 :

Minimum

(\frac{π}{2} + 2 πn, - 4),

Minimum

(\frac{3 π}{2} + 2 πn, - 6)

Popular Examples

f (x) = 3 x^{2} + 9 x - 2

f (x) = 3 x^{2} + 9 x - 7

f (x) = 3 x^{2} + 9 x + 8

y = - 2 (x - 3)^{2} + 2

y = 3 (x + 4)^{2} - 9

Frequently Asked Questions (FAQ)

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