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Popular >

f(x)=2(csc(x)+sec(x))

Solution

f (x) = 2 (csc (x) + sec (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{3 π}{4} + 2 πn, 0), (\frac{7 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 : Minimum (\frac{π}{4} + 2 πn, 42), Maximum (\frac{5 π}{4} + 2 πn, - 42)

+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

2 (csc (x) + sec (x)) : 2 π

Domain of

2 (csc (x) + sec (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

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

Axis interception points of

2 (csc (x) + sec (x)) :

X Intercepts

: (\frac{3 π}{4} + 2 πn, 0), (\frac{7 π}{4} + 2 πn, 0)

Asymptotes of

2 (csc (x) + sec (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

2 (csc (x) + sec (x)) :

Minimum

(\frac{π}{4} + 2 πn, 42),

Maximum

(\frac{5 π}{4} + 2 πn, - 42)

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