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Popular >

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

Solution

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

Solution

Period : 2 π

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

Range : f (x) \leq 0

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

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

Extreme Points : Maximum (\frac{π}{2} + 2 πn, 0)

+1

Interval Notation

Domain : [2 πn, \frac{3 π}{2} + 2 πn) \cup (\frac{3 π}{2} + 2 πn, 2 π + 2 πn)

Range : (- \infty, 0]

Solution steps

Periodicity of

\frac{sin ( x ) - 1}{sin ( x ) + 1} : 2 π

Domain of

\frac{sin ( x ) - 1}{sin ( x ) + 1} : 2 πn \leq x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Range of

\frac{sin ( x ) - 1}{sin ( x ) + 1} : f (x) \leq 0

Axis interception points of

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

X Intercepts

: (\frac{π}{2} + 2 πn, 0),

Y Intercepts

: (0, - 1)

Asymptotes of

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

Vertical

: x = \frac{3 π}{2} + 2 πn

Extreme Points of

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

Maximum

(\frac{π}{2} + 2 πn, 0)

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Frequently Asked Questions (FAQ)

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