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Popular >

f(x)=3sin(x)-4sin^3(x)

Solution

f (x) = 3 sin (x) - 4 sin^{3} (x)

Solution

Period : 2 π

Domain : - \infty < x < \infty

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

X Intercepts : (2 πn, 0), (π + 2 πn, 0), (\frac{4 π}{3} + 2 πn, 0), (\frac{5 π}{3} + 2 πn, 0), (\frac{π}{3} + 2 πn, 0), (\frac{2 π}{3} + 2 πn, 0), Y Intercepts : (0, 0)

Asymptotes : None

Extreme Points : Maximum (\frac{π}{6} + 2 πn, 1), Minimum (\frac{π}{2} + 2 πn, - 1), Maximum (\frac{5 π}{6} + 2 πn, 1), Minimum (\frac{7 π}{6} + 2 πn, - 1), Maximum (\frac{3 π}{2} + 2 πn, 1), Minimum (\frac{11 π}{6} + 2 πn, - 1)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 1, 1]

Solution steps

Periodicity of

3 sin (x) - 4 sin^{3} (x) : 2 π

Domain of

3 sin (x) - 4 sin^{3} (x) : - \infty < x < \infty

Range of

3 sin (x) - 4 sin^{3} (x) : - 1 \leq f (x) \leq 1

Axis interception points of

3 sin (x) - 4 sin^{3} (x) :

X Intercepts

: (2 πn, 0), (π + 2 πn, 0), (\frac{4 π}{3} + 2 πn, 0), (\frac{5 π}{3} + 2 πn, 0), (\frac{π}{3} + 2 πn, 0), (\frac{2 π}{3} + 2 πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

3 sin (x) - 4 sin^{3} (x) :

None

Extreme Points of

3 sin (x) - 4 sin^{3} (x) :

Maximum

(\frac{π}{6} + 2 πn, 1),

Minimum

(\frac{π}{2} + 2 πn, - 1),

Maximum

(\frac{5 π}{6} + 2 πn, 1),

Minimum

(\frac{7 π}{6} + 2 πn, - 1),

Maximum

(\frac{3 π}{2} + 2 πn, 1),

Minimum

(\frac{11 π}{6} + 2 πn, - 1)

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Frequently Asked Questions (FAQ)

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