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Popular >

y= 1/((sin^2(x)+2sin(x)+2))

Solution

y = \frac{1}{( sin ^{2} ( x ) + 2 sin ( x ) + 2 )}

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : \frac{1}{5} \leq f (x) \leq 1

Y Intercepts : (0, \frac{1}{2})

Asymptotes : None

Extreme Points : Minimum (\frac{π}{2} + 2 πn, \frac{1}{5}), Maximum (\frac{3 π}{2} + 2 πn, 1)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [\frac{1}{5}, 1]

Solution steps

Periodicity of

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

Domain of

\frac{1}{sin ^{2} ( x ) + 2 sin ( x ) + 2} : - \infty < x < \infty

Range of

\frac{1}{sin ^{2} ( x ) + 2 sin ( x ) + 2} : \frac{1}{5} \leq f (x) \leq 1

Axis interception points of

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

Y Intercepts

: (0, \frac{1}{2})

Asymptotes of

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

None

Extreme Points of

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

Minimum

(\frac{π}{2} + 2 πn, \frac{1}{5}),

Maximum

(\frac{3 π}{2} + 2 πn, 1)

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Frequently Asked Questions (FAQ)

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