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Popular >

f(x)= 8/(sin(x)+cos(x))

Solution

f (x) = \frac{8}{sin ( x ) + cos ( x )}

Solution

Period : 2 π

Domain : 2 πn \leq x < \frac{3 π}{4} + 2 πn or \frac{3 π}{4} + 2 πn < x < \frac{7 π}{4} + 2 πn or \frac{7 π}{4} + 2 πn < x < 2 π + 2 πn

Range : f (x) \leq - 42 or f (x) \geq 42

Y Intercepts : (0, 8)

Asymptotes : Vertical x = \frac{3 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Extreme Points : Minimum (\frac{π}{4} + 2 πn, 42), Maximum (\frac{5 π}{4} + 2 πn, - 42)

+1

Interval Notation

Range : (- \infty, - 42] \cup [42, \infty)

Solution steps

Periodicity of

\frac{8}{sin ( x ) + cos ( x )} : 2 π

Domain of

\frac{8}{sin ( x ) + cos ( x )} : 2 πn \leq x < \frac{3 π}{4} + 2 πn or \frac{3 π}{4} + 2 πn < x < \frac{7 π}{4} + 2 πn or \frac{7 π}{4} + 2 πn < x < 2 π + 2 πn

Range of

\frac{8}{sin ( x ) + cos ( x )} : f (x) \leq - 42 or f (x) \geq 42

Axis interception points of

\frac{8}{sin ( x ) + cos ( x )} :

Y Intercepts

: (0, 8)

Asymptotes of

\frac{8}{sin ( x ) + cos ( x )} :

Vertical

: x = \frac{3 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Extreme Points of

\frac{8}{sin ( x ) + cos ( x )} :

Minimum

(\frac{π}{4} + 2 πn, 42),

Maximum

(\frac{5 π}{4} + 2 πn, - 42)

Graph

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Frequently Asked Questions (FAQ)

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