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Popular >

y=cos^2(3x+1)

Solution

y = cos^{2} (3 x + 1)

Solution

Period : \frac{π}{3}

Domain : - \infty < x < \infty

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

X Intercepts : (- \frac{1}{3} + \frac{π}{6} + \frac{πn}{3}, 0), (- \frac{1}{3} + \frac{π}{6} + \frac{πn}{3}, 0), Y Intercepts : (0, cos^{2} (3 \cdot 0 + 1))

Asymptotes : None

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

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [0, 1]

Solution steps

Periodicity of

cos^{2} (3 x + 1) : \frac{π}{3}

Domain of

cos^{2} (3 x + 1) : - \infty < x < \infty

Range of

cos^{2} (3 x + 1) : 0 \leq f (x) \leq 1

Axis interception points of

cos^{2} (3 x + 1) :

X Intercepts

: (- \frac{1}{3} + \frac{π}{6} + \frac{πn}{3}, 0), (- \frac{1}{3} + \frac{π}{6} + \frac{πn}{3}, 0),

Y Intercepts

: (0, cos^{2} (3 \cdot 0 + 1))

Asymptotes of

cos^{2} (3 x + 1) :

None

Extreme Points of

cos^{2} (3 x + 1) :

Minimum

(- \frac{1}{3} + \frac{π}{6} + \frac{π}{3} n, 0),

Minimum

(\frac{- 2 + π}{6} + \frac{π}{3} n, 0),

Maximum

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

Maximum

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

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Frequently Asked Questions (FAQ)

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