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Popular >

f(θ)=sin^4(θ)+cos^4(θ)

Solution

f (θ) = sin^{4} (θ) + cos^{4} (θ)

Solution

Period : π

Domain : - \infty < θ < \infty

Range : \frac{1}{2} \leq f (θ) \leq 1

Y Intercepts : (0, 1)

Asymptotes : None

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

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [\frac{1}{2}, 1]

Solution steps

Periodicity of

sin^{4} (θ) + cos^{4} (θ) : π

Domain of

sin^{4} (θ) + cos^{4} (θ) : - \infty < θ < \infty

Range of

sin^{4} (θ) + cos^{4} (θ) : \frac{1}{2} \leq f (θ) \leq 1

Axis interception points of

sin^{4} (θ) + cos^{4} (θ) :

Y Intercepts

: (0, 1)

Asymptotes of

sin^{4} (θ) + cos^{4} (θ) :

None

Extreme Points of

sin^{4} (θ) + cos^{4} (θ) :

Maximum

(πn, 1),

Minimum

(\frac{π}{4} + πn, \frac{1}{2}),

Maximum

(\frac{π}{2} + πn, 1),

Minimum

(\frac{3 π}{4} + πn, \frac{1}{2})

Popular Examples

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y=sin(sin(sin(x)))

y = sin (sin (sin (x)))

Frequently Asked Questions (FAQ)

What is the f(θ)=sin^4(θ)+cos^4(θ) ?
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