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Popular >

f(x)=(tan(x)-5)/(sec(x))

Solution

f (x) = \frac{tan ( x ) - 5}{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 : - \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + 2 π )} \leq f (x) \leq - \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + π )}

X Intercepts : (arctan (5) + 2 πn, 0), (arctan (5) + π + 2 πn, 0), Y Intercepts : (0, - 5)

Asymptotes : None

Extreme Points : Maximum (- arctan (\frac{1}{5}) + π + 2 πn, - \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + π )}), Minimum (- arctan (\frac{1}{5}) + 2 π + 2 πn, - \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + 2 π )})

+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 : [- \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + 2 π )}, - \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + π )}]

Solution steps

Periodicity of

\frac{tan ( x ) - 5}{sec ( x )} : 2 π

Domain of

\frac{tan ( x ) - 5}{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 ) - 5}{sec ( x )} : - \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + 2 π )} \leq f (x) \leq - \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + π )}

Axis interception points of

\frac{tan ( x ) - 5}{sec ( x )} :

X Intercepts

: (arctan (5) + 2 πn, 0), (arctan (5) + π + 2 πn, 0),

Y Intercepts

: (0, - 5)

Asymptotes of

\frac{tan ( x ) - 5}{sec ( x )} :

None

Extreme Points of

\frac{tan ( x ) - 5}{sec ( x )} :

Maximum

(- arctan (\frac{1}{5}) + π + 2 πn, - \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + π )}),

Minimum

(- arctan (\frac{1}{5}) + 2 π + 2 πn, - \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + 2 π )})

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Frequently Asked Questions (FAQ)

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