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Popular >

y=3cos(x+pi/3)

Solution

y = 3 cos (x + \frac{π}{3})

Solution

Period : 2 π

Domain : - \infty < x < \infty

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

X Intercepts : (\frac{π}{6} + 2 πn, 0), (\frac{7 π}{6} + 2 πn, 0), Y Intercepts : (0, \frac{3}{2})

Asymptotes : None

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

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 3, 3]

Solution steps

Periodicity of

3 cos (x + \frac{π}{3}) : 2 π

Domain of

3 cos (x + \frac{π}{3}) : - \infty < x < \infty

Range of

3 cos (x + \frac{π}{3}) : - 3 \leq f (x) \leq 3

Axis interception points of

3 cos (x + \frac{π}{3}) :

X Intercepts

: (\frac{π}{6} + 2 πn, 0), (\frac{7 π}{6} + 2 πn, 0),

Y Intercepts

: (0, \frac{3}{2})

Asymptotes of

3 cos (x + \frac{π}{3}) :

None

Extreme Points of

3 cos (x + \frac{π}{3}) :

Minimum

(\frac{2 π}{3} + 2 πn, - 3),

Maximum

(\frac{5 π}{3} + 2 πn, 3)

Popular Examples

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f (x) = 2 x^{4} + 5 x^{3} - 11 x^{2} - 204 x + 12

f (x) = - 5 x - 5

f(θ)=2+2sin(θ)

f (θ) = 2 + 2 sin (θ)

f (x) = ln (3) x^{2}

Frequently Asked Questions (FAQ)

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