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Popular >

f(θ)=(12)/(1-2cos(θ))

Solution

f (θ) = \frac{12}{1 - 2 cos ( θ )}

Solution

Period : 2 π

Domain : 2 πn \leq θ < \frac{π}{3} + 2 πn or \frac{π}{3} + 2 πn < θ < \frac{5 π}{3} + 2 πn or \frac{5 π}{3} + 2 πn < θ < 2 π + 2 πn

Range : f (θ) \leq - 12 or f (θ) \geq 4

Y Intercepts : (0, - 12)

Asymptotes : Vertical θ = \frac{5 π}{3} + 2 πn, θ = \frac{π}{3} + 2 πn

Extreme Points : Maximum (2 πn, - 12), Minimum (π + 2 πn, 4)

+1

Interval Notation

Domain : [2 πn, \frac{π}{3} + 2 πn) \cup (\frac{π}{3} + 2 πn, \frac{5 π}{3} + 2 πn) \cup (\frac{5 π}{3} + 2 πn, 2 π + 2 πn)

Range : (- \infty, - 12] \cup [4, \infty)

Solution steps

Periodicity of

\frac{12}{1 - 2 cos ( θ )} : 2 π

Domain of

\frac{12}{1 - 2 cos ( θ )} : 2 πn \leq θ < \frac{π}{3} + 2 πn or \frac{π}{3} + 2 πn < θ < \frac{5 π}{3} + 2 πn or \frac{5 π}{3} + 2 πn < θ < 2 π + 2 πn

Range of

\frac{12}{1 - 2 cos ( θ )} : f (θ) \leq - 12 or f (θ) \geq 4

Axis interception points of

\frac{12}{1 - 2 cos ( θ )} :

Y Intercepts

: (0, - 12)

Asymptotes of

\frac{12}{1 - 2 cos ( θ )} :

Vertical

: θ = \frac{5 π}{3} + 2 πn, θ = \frac{π}{3} + 2 πn

Extreme Points of

\frac{12}{1 - 2 cos ( θ )} :

Maximum

(2 πn, - 12),

Minimum

(π + 2 πn, 4)

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Frequently Asked Questions (FAQ)

What is the f(θ)=(12)/(1-2cos(θ)) ?
The f(θ)=(12)/(1-2cos(θ)) is