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Popular >

f(x)= 1/(cos(x)-sin(x))

Solution

f (x) = \frac{1}{cos ( x ) - sin ( x )}

Solution

Period : 2 π

Domain : 2 πn \leq x < \frac{π}{4} + 2 πn or \frac{π}{4} + 2 πn < x < \frac{5 π}{4} + 2 πn or \frac{5 π}{4} + 2 πn < x < 2 π + 2 πn

Range : f (x) \leq - \frac{1}{2} or f (x) \geq \frac{1}{2}

Y Intercepts : (0, 1)

Asymptotes : Vertical x = \frac{5 π}{4} + 2 πn, x = \frac{π}{4} + 2 πn

Extreme Points : Maximum (\frac{3 π}{4} + 2 πn, - \frac{1}{2}), Minimum (\frac{7 π}{4} + 2 πn, \frac{1}{2})

+1

Interval Notation

Domain : [2 πn, \frac{π}{4} + 2 πn) \cup (\frac{π}{4} + 2 πn, \frac{5 π}{4} + 2 πn) \cup (\frac{5 π}{4} + 2 πn, 2 π + 2 πn)

Range : (- \infty, - \frac{1}{2}] \cup [\frac{1}{2}, \infty)

Solution steps

Periodicity of

\frac{1}{cos ( x ) - sin ( x )} : 2 π

Domain of

\frac{1}{cos ( x ) - sin ( x )} : 2 πn \leq x < \frac{π}{4} + 2 πn or \frac{π}{4} + 2 πn < x < \frac{5 π}{4} + 2 πn or \frac{5 π}{4} + 2 πn < x < 2 π + 2 πn

Range of

\frac{1}{cos ( x ) - sin ( x )} : f (x) \leq - \frac{1}{2} or f (x) \geq \frac{1}{2}

Axis interception points of

\frac{1}{cos ( x ) - sin ( x )} :

Y Intercepts

: (0, 1)

Asymptotes of

\frac{1}{cos ( x ) - sin ( x )} :

Vertical

: x = \frac{5 π}{4} + 2 πn, x = \frac{π}{4} + 2 πn

Extreme Points of

\frac{1}{cos ( x ) - sin ( x )} :

Maximum

(\frac{3 π}{4} + 2 πn, - \frac{1}{2}),

Minimum

(\frac{7 π}{4} + 2 πn, \frac{1}{2})

Popular Examples

y=(2/3)^{x-3}-2

y = (\frac{2}{3})^{x - 3} - 2

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f (x) = \frac{372}{53 + 40 cos ( x ) + 9 sin ( x )}

f(x)=-log_{10}(3)(x+1)

f (x) = - lo g_{10} (3) (x + 1)

Frequently Asked Questions (FAQ)

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