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Popular Calculus >

f(x)=sin^4(3x+5)

Solution

f (x) = sin^{4} (3 x + 5)

Solution

Period : \frac{π}{3}

Domain : - \infty < x < \infty

Range : 0 \leq f (x) \leq 1

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

Asymptotes : None

Extreme Points : Minimum (\frac{- 5 + 2 π}{3} + \frac{π}{3} n, 0), Minimum (\frac{2 π - 5}{3} + \frac{π}{3} n, 0), Maximum (\frac{- 10 + 5 π}{6} + \frac{π}{3} n, 1)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [0, 1]

Solution steps

Periodicity of

sin^{4} (3 x + 5) : \frac{π}{3}

Domain of

sin^{4} (3 x + 5) : - \infty < x < \infty

Range of

sin^{4} (3 x + 5) : 0 \leq f (x) \leq 1

Axis interception points of

sin^{4} (3 x + 5) :

X Intercepts

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

Y Intercepts

: (0, sin^{4} (3 \cdot 0 + 5))

Asymptotes of

sin^{4} (3 x + 5) :

None

Extreme Points of

sin^{4} (3 x + 5) :

Minimum

(\frac{- 5 + 2 π}{3} + \frac{π}{3} n, 0),

Minimum

(\frac{2 π - 5}{3} + \frac{π}{3} n, 0),

Maximum

(\frac{- 10 + 5 π}{6} + \frac{π}{3} n, 1)

Graph

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Frequently Asked Questions (FAQ)

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