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Popular Calculus >

f(x)=((tan(x)-1))/(sec(x))

Solution

f (x) = \frac{( tan ( x ) - 1 )}{sec ( 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 : - 2 \leq f (x) \leq 2

X Intercepts : (\frac{π}{4} + 2 πn, 0), (\frac{5 π}{4} + 2 πn, 0), Y Intercepts : (0, - 1)

Asymptotes : None

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

+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 : [- 2, 2]

Solution steps

Periodicity of

\frac{tan ( x ) - 1}{sec ( x )} : 2 π

Domain of

\frac{tan ( x ) - 1}{sec ( 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{tan ( x ) - 1}{sec ( x )} : - 2 \leq f (x) \leq 2

Axis interception points of

\frac{tan ( x ) - 1}{sec ( x )} :

X Intercepts

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

Y Intercepts

: (0, - 1)

Asymptotes of

\frac{tan ( x ) - 1}{sec ( x )} :

None

Extreme Points of

\frac{tan ( x ) - 1}{sec ( x )} :

Maximum

(\frac{3 π}{4} + 2 πn, 2),

Minimum

(\frac{7 π}{4} + 2 πn, - 2)

Graph

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Frequently Asked Questions (FAQ)

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