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Popular >

y=(sin^3(x)+5)/(cos(x))

Solution

y = \frac{sin ^{3} ( x ) + 5}{cos ( x )}

Solution

Period : 2 π

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

Range : f (x) \leq - 5 or f (x) \geq 5

Y Intercepts : (0, 5)

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

Extreme Points : Minimum (2 πn, 5), Maximum (π + 2 πn, - 5)

+1

Interval Notation

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

Range : (- \infty, - 5] \cup [5, \infty)

Solution steps

Periodicity of

\frac{sin ^{3} ( x ) + 5}{cos ( x )} : 2 π

Domain of

\frac{sin ^{3} ( x ) + 5}{cos ( x )} : 2 πn \leq x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Range of

\frac{sin ^{3} ( x ) + 5}{cos ( x )} : f (x) \leq - 5 or f (x) \geq 5

Axis interception points of

\frac{sin ^{3} ( x ) + 5}{cos ( x )} :

Y Intercepts

: (0, 5)

Asymptotes of

\frac{sin ^{3} ( x ) + 5}{cos ( x )} :

Vertical

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

Extreme Points of

\frac{sin ^{3} ( x ) + 5}{cos ( x )} :

Minimum

(2 πn, 5),

Maximum

(π + 2 πn, - 5)

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Frequently Asked Questions (FAQ)

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