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Popular >

f(x)=sec(x)-csc(x)

Solution

f (x) = sec (x) - csc (x)

Solution

Period : 2 π

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

Range : - \infty < f (x) < \infty

X Intercepts : (\frac{π}{4} + 2 πn, 0), (\frac{5 π}{4} + 2 πn, 0)

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

Extreme Points : Maximum (\frac{3 π}{4} + 2 πn, - 22), Minimum (\frac{7 π}{4} + 2 πn, 22)

+1

Interval Notation

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

Range : (- \infty, \infty)

Solution steps

Periodicity of

sec (x) - csc (x) : 2 π

Domain of

sec (x) - csc (x) : 2 πn < x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < π + 2 πn or π + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Range of

sec (x) - csc (x) : - \infty < f (x) < \infty

Axis interception points of

sec (x) - csc (x) :

X Intercepts

: (\frac{π}{4} + 2 πn, 0), (\frac{5 π}{4} + 2 πn, 0)

Asymptotes of

sec (x) - csc (x) :

Vertical

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

Extreme Points of

sec (x) - csc (x) :

Maximum

(\frac{3 π}{4} + 2 πn, - 22),

Minimum

(\frac{7 π}{4} + 2 πn, 22)

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