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Popular >

f(θ)=cos(θ)cot(θ)

Solution

f (θ) = cos (θ) cot (θ)

Solution

Period : 2 π

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

Range : - \infty < f (θ) < \infty

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

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

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

+1

Interval Notation

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

Range : (- \infty, \infty)

Solution steps

Periodicity of

cos (θ) cot (θ) : 2 π

Domain of

cos (θ) cot (θ) : 2 πn < θ < π + 2 πn or π + 2 πn < θ < 2 π + 2 πn

Range of

cos (θ) cot (θ) : - \infty < f (θ) < \infty

Axis interception points of

cos (θ) cot (θ) :

X Intercepts

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

Asymptotes of

cos (θ) cot (θ) :

Vertical

: θ = 2 πn, θ = π + 2 πn

Extreme Points of

cos (θ) cot (θ) :

Minimum

(\frac{π}{2} + 2 πn, 0),

Maximum

(\frac{3 π}{2} + 2 πn, 0)

Popular Examples

y = x^{2} - 25

g(x)=-5cos(2x+2pi)

g (x) = - 5 cos (2 x + 2 π)

s (t) = 5 t + 45

f (x) = - 3 x + \frac{1}{2}

y = (\frac{1}{8})^{x}

Frequently Asked Questions (FAQ)

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