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Popular >

f(θ)= 6/(2cos(θ)-3sin(θ))

Solution

f (θ) = \frac{6}{2 cos ( θ ) - 3 sin ( θ )}

Solution

Period : 2 π

Domain : 2 πn \leq θ < 0.58800 \dots + 2 πn or 0.58800 \dots + 2 πn < θ < 0.58800 \dots + π + 2 πn or 0.58800 \dots + π + 2 πn < θ < 2 π + 2 πn

Range : f (θ) \leq - \frac{6}{13} or f (θ) \geq \frac{6}{13}

Y Intercepts : (0, 3)

Asymptotes : Vertical θ = 0.58800 \dots + 2 πn, θ = 0.58800 \dots + π + 2 πn

Extreme Points : Maximum (- arctan (\frac{3}{2}) + π + 2 πn, - \frac{6}{13}), Minimum (- arctan (\frac{3}{2}) + 2 π + 2 πn, \frac{6}{13})

+1

Solution steps

Periodicity of

\frac{6}{2 cos ( θ ) - 3 sin ( θ )} : 2 π

Domain of

\frac{6}{2 cos ( θ ) - 3 sin ( θ )} : 2 πn \leq θ < 0.58800 \dots + 2 πn or 0.58800 \dots + 2 πn < θ < 0.58800 \dots + π + 2 πn or 0.58800 \dots + π + 2 πn < θ < 2 π + 2 πn

Range of

\frac{6}{2 cos ( θ ) - 3 sin ( θ )} : f (θ) \leq - \frac{6}{13} or f (θ) \geq \frac{6}{13}

Axis interception points of

\frac{6}{2 cos ( θ ) - 3 sin ( θ )} :

Y Intercepts

: (0, 3)

Asymptotes of

\frac{6}{2 cos ( θ ) - 3 sin ( θ )} :

Vertical

: θ = 0.58800 \dots + 2 πn, θ = 0.58800 \dots + π + 2 πn

Extreme Points of

\frac{6}{2 cos ( θ ) - 3 sin ( θ )} :

Maximum

(- arctan (\frac{3}{2}) + π + 2 πn, - \frac{6}{13}),

Minimum

(- arctan (\frac{3}{2}) + 2 π + 2 πn, \frac{6}{13})

Popular Examples

f(x)=(x^2+7x+3)/(x^2)

f (x) = \frac{x ^{2} + 7 x + 3}{x ^{2}}

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f(x)=2x^{5/3}-3x^{2/3}

f (x) = 2 x^{\frac{5}{3}} - 3 x^{\frac{2}{3}}

y = - 2 x^{2} + x - 1

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

Frequently Asked Questions (FAQ)

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