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Popular Calculus >

f(θ)=3cos(θ)

Solution

f (θ) = 3 cos (θ)

Solution

Period : 2 π

Domain : - \infty < θ < \infty

Range : - 3 \leq f (θ) \leq 3

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

Asymptotes : None

Extreme Points : Maximum (2 πn, 3), Minimum (π + 2 πn, - 3)

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Interval Notation

Domain : (- \infty, \infty)

Range : [- 3, 3]

Solution steps

Periodicity of

3 cos (θ) : 2 π

Domain of

3 cos (θ) : - \infty < θ < \infty

Range of

3 cos (θ) : - 3 \leq f (θ) \leq 3

Axis interception points of

3 cos (θ) :

X Intercepts

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

Y Intercepts

: (0, 3)

Asymptotes of

3 cos (θ) :

None

Extreme Points of

3 cos (θ) :

Maximum

(2 πn, 3),

Minimum

(π + 2 πn, - 3)

Graph

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