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Popular >

f(θ)=cos(3θ),0<= θ<= 2pi

Solution

f (θ) = cos (3 θ), 0 \leq θ \leq 2 π

Solution

Period : \frac{2 π}{3}

Domain : 0 \leq θ \leq 2 π

Range : - 1 \leq f (θ) \leq 1

X Intercepts : (\frac{π}{6}, 0), (\frac{π}{2}, 0), (\frac{5 π}{6}, 0), (\frac{7 π}{6}, 0), (\frac{3 π}{2}, 0), (\frac{11 π}{6}, 0), Y Intercepts : (0, 1)

Asymptotes : None

Extreme Points : Maximum (0, 1), Minimum (\frac{π}{3}, - 1), Maximum (\frac{2 π}{3}, 1), Minimum (π, - 1), Maximum (\frac{4 π}{3}, 1), Minimum (\frac{5 π}{3}, - 1), Maximum (2 π, 1)

+1

Interval Notation

Domain : [0, 2 π]

Range : [- 1, 1]

Solution steps

Periodicity of

cos (3 θ) : \frac{2 π}{3}

Domain of

cos (3 θ), 0 \leq θ \leq 2 π : 0 \leq θ \leq 2 π

Range of

cos (3 θ), 0 \leq θ \leq 2 π : - 1 \leq f (θ) \leq 1

Axis interception points of

cos (3 θ), 0 \leq θ \leq 2 π :

X Intercepts

: (\frac{π}{6}, 0), (\frac{π}{2}, 0), (\frac{5 π}{6}, 0), (\frac{7 π}{6}, 0), (\frac{3 π}{2}, 0), (\frac{11 π}{6}, 0),

Y Intercepts

: (0, 1)

Asymptotes of

cos (3 θ), 0 \leq θ \leq 2 π :

None

Extreme Points of

cos (3 θ), 0 \leq θ \leq 2 π :

Maximum

(0, 1),

Minimum

(\frac{π}{3}, - 1),

Maximum

(\frac{2 π}{3}, 1),

Minimum

(π, - 1),

Maximum

(\frac{4 π}{3}, 1),

Minimum

(\frac{5 π}{3}, - 1),

Maximum

(2 π, 1)

Popular Examples

f(x)=(3x)/(x+3)

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y = - 3 cos (x)

y = 2 x + 3

f (x) = 5 x - 12

Frequently Asked Questions (FAQ)

What is the f(θ)=cos(3θ),0<= θ<= 2pi ?
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