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Popular >

f(θ)=cos^3(θ)+sin^3(θ)

Solution

f (θ) = cos^{3} (θ) + sin^{3} (θ)

Solution

Period : 2 π

Domain : - \infty < θ < \infty

Range : - 1 \leq f (θ) \leq 1

X Intercepts : (\frac{3 π}{4} + 2 πn, 0), (\frac{7 π}{4} + 2 πn, 0), Y Intercepts : (0, 1)

Asymptotes : None

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

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 1, 1]

Solution steps

Periodicity of

cos^{3} (θ) + sin^{3} (θ) : 2 π

Domain of

cos^{3} (θ) + sin^{3} (θ) : - \infty < θ < \infty

Range of

cos^{3} (θ) + sin^{3} (θ) : - 1 \leq f (θ) \leq 1

Axis interception points of

cos^{3} (θ) + sin^{3} (θ) :

X Intercepts

: (\frac{3 π}{4} + 2 πn, 0), (\frac{7 π}{4} + 2 πn, 0),

Y Intercepts

: (0, 1)

Asymptotes of

cos^{3} (θ) + sin^{3} (θ) :

None

Extreme Points of

cos^{3} (θ) + sin^{3} (θ) :

Maximum

(2 πn, 1),

Minimum

(\frac{π}{4} + 2 πn, \frac{1}{2}),

Maximum

(\frac{π}{2} + 2 πn, 1),

Minimum

(π + 2 πn, - 1),

Maximum

(\frac{5 π}{4} + 2 πn, - \frac{1}{2}),

Minimum

(\frac{3 π}{2} + 2 πn, - 1)

Popular Examples

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Frequently Asked Questions (FAQ)

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