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Popular >

y= 4/((3sin(x)+4cos(x)-2))

Solution

y = \frac{4}{( 3 sin ( x ) + 4 cos ( x ) - 2 )}

Solution

Period : 2 π

Domain : 2 πn \leq x < π - 1.33881 \dots + 2 πn or π - 1.33881 \dots + 2 πn < x < 5.76740 \dots + 2 πn or 5.76740 \dots + 2 πn < x < 2 π + 2 πn

Range : f (x) \leq - \frac{4}{7} or f (x) \geq \frac{4}{3}

Y Intercepts : (0, 2)

Asymptotes : Vertical x = 5.76740 \dots + 2 πn, x = π - 1.33881 \dots + 2 πn

Extreme Points : Minimum (arctan (\frac{3}{4}) + 2 πn, \frac{4}{3}), Maximum (arctan (\frac{3}{4}) + π + 2 πn, - \frac{4}{7})

+1

Interval Notation

Domain : [2 πn, π - 1.33881 \dots + 2 πn) \cup (π - 1.33881 \dots + 2 πn, 5.76740 \dots + 2 πn) \cup (5.76740 \dots + 2 πn, 2 π + 2 πn)

Range : (- \infty, - \frac{4}{7}] \cup [\frac{4}{3}, \infty)

Solution steps

Periodicity of

\frac{4}{3 sin ( x ) + 4 cos ( x ) - 2} : 2 π

Domain of

\frac{4}{3 sin ( x ) + 4 cos ( x ) - 2} : 2 πn \leq x < π - 1.33881 \dots + 2 πn or π - 1.33881 \dots + 2 πn < x < 5.76740 \dots + 2 πn or 5.76740 \dots + 2 πn < x < 2 π + 2 πn

Range of

\frac{4}{3 sin ( x ) + 4 cos ( x ) - 2} : f (x) \leq - \frac{4}{7} or f (x) \geq \frac{4}{3}

Axis interception points of

\frac{4}{3 sin ( x ) + 4 cos ( x ) - 2} :

Y Intercepts

: (0, 2)

Asymptotes of

\frac{4}{3 sin ( x ) + 4 cos ( x ) - 2} :

Vertical

: x = 5.76740 \dots + 2 πn, x = π - 1.33881 \dots + 2 πn

Extreme Points of

\frac{4}{3 sin ( x ) + 4 cos ( x ) - 2} :

Minimum

(arctan (\frac{3}{4}) + 2 πn, \frac{4}{3}),

Maximum

(arctan (\frac{3}{4}) + π + 2 πn, - \frac{4}{7})

Popular Examples

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f (x) = 27 x^{3} + 27 x^{2} + 3 x + 1

f (- 2) = x^{2} - x

Frequently Asked Questions (FAQ)

What is the y= 4/((3sin(x)+4cos(x)-2)) ?
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