en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

f(θ)=csc^2(θ)-cot(θ)-3

Solution

f (θ) = csc^{2} (θ) - cot (θ) - 3

Solution

Period : π

Domain : πn < θ < π + πn

Range : f (θ) \geq - \frac{9}{4}

X Intercepts : (arccot (2) + πn, 0), (\frac{3 π}{4} + πn, 0)

Asymptotes : Vertical θ = πn

Extreme Points : Minimum (arccot (\frac{1}{2}) + πn, - \frac{9}{4})

+1

Interval Notation

Domain : (πn, π + πn)

Range : [- \frac{9}{4}, \infty)

Solution steps

Periodicity of

csc^{2} (θ) - cot (θ) - 3 : π

Domain of

csc^{2} (θ) - cot (θ) - 3 : πn < θ < π + πn

Range of

csc^{2} (θ) - cot (θ) - 3 : f (θ) \geq - \frac{9}{4}

Axis interception points of

csc^{2} (θ) - cot (θ) - 3 :

X Intercepts

: (arccot (2) + πn, 0), (\frac{3 π}{4} + πn, 0)

Asymptotes of

csc^{2} (θ) - cot (θ) - 3 :

Vertical

: θ = πn

Extreme Points of

csc^{2} (θ) - cot (θ) - 3 :

Minimum

(arccot (\frac{1}{2}) + πn, - \frac{9}{4})

Popular Examples

y = ln (e^{x} + x e^{x})

h(t)=-4.9t^2+t+21

h (t) = - 4.9 t^{2} + t + 21

y = \frac{x}{∣ x ∣}

f(x)=\sqrt[4]{x-2}

f(x)=x^3+2x^2-16x-32

f (x) = x^{3} + 2 x^{2} - 16 x - 32

Frequently Asked Questions (FAQ)

What is the f(θ)=csc^2(θ)-cot(θ)-3 ?
The f(θ)=csc^2(θ)-cot(θ)-3 is