What is the y=sin^2(x)+sin^4(x)+sin^6(x) ?

The y=sin^2(x)+sin^4(x)+sin^6(x) is

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y=sin^2(x)+sin^4(x)+sin^6(x)

y = sin^{2} (x) + sin^{4} (x) + sin^{6} (x)

Period : π

Domain : - \infty < x < \infty

Range : 0 \leq f (x) \leq 3

X Intercepts : (πn, 0), Y Intercepts : (0, 0)

Asymptotes : None

Extreme Points : Minimum (πn, 0), Maximum (\frac{π}{2} + πn, 3)

Interval Notation

Domain : (- \infty, \infty)

Range : [0, 3]

Solution steps

Periodicity of

sin^{2} (x) + sin^{4} (x) + sin^{6} (x) : π

Domain of

sin^{2} (x) + sin^{4} (x) + sin^{6} (x) : - \infty < x < \infty

Range of

sin^{2} (x) + sin^{4} (x) + sin^{6} (x) : 0 \leq f (x) \leq 3

Axis interception points of

sin^{2} (x) + sin^{4} (x) + sin^{6} (x) :

X Intercepts

: (πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

sin^{2} (x) + sin^{4} (x) + sin^{6} (x) :

None

Extreme Points of

sin^{2} (x) + sin^{4} (x) + sin^{6} (x) :

Minimum

(πn, 0),

Maximum

(\frac{π}{2} + πn, 3)