What is the f(x)=(sin(x))/((1+cos^2(x))) ?

The f(x)=(sin(x))/((1+cos^2(x))) is

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f(x)=(sin(x))/((1+cos^2(x)))

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

Period : 2 π

Domain : - \infty < x < \infty

Range : - 1 \leq f (x) \leq 1

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

Asymptotes : None

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

Interval Notation

Domain : (- \infty, \infty)

Range : [- 1, 1]

Solution steps

Periodicity of

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

Domain of

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

Range of

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

Axis interception points of

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

X Intercepts

: (2 πn, 0), (π + 2 πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

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

None

Extreme Points of

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

Maximum

(\frac{π}{2} + 2 πn, 1),

Minimum

(\frac{3 π}{2} + 2 πn, - 1)

f (a) = 729 a^{3} + 81 a^{2} + 27 a + 1

h (t) = - 5 t^{2} + 8 t

f (x) = 3 x^{2} + 12 x - 7

y = tan^{3} (x) - tan (x)

f (x) = x^{2} - 38 x - 324