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Popular >

f(x)=sec^3(x)

Solution

f (x) = sec^{3} (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 - 1 or f (x) \geq 1

Y Intercepts : (0, 1)

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

Extreme Points : Minimum (2 πn, 1), Maximum (π + 2 πn, - 1)

+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, - 1] \cup [1, \infty)

Solution steps

Periodicity of

sec^{3} (x) : 2 π

Domain of

sec^{3} (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

sec^{3} (x) : f (x) \leq - 1 or f (x) \geq 1

Axis interception points of

sec^{3} (x) :

Y Intercepts

: (0, 1)

Asymptotes of

sec^{3} (x) :

Vertical

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

Extreme Points of

sec^{3} (x) :

Minimum

(2 πn, 1),

Maximum

(π + 2 πn, - 1)

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Frequently Asked Questions (FAQ)

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