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Popular >

f(t)=cos^4(t)+sin^4(t)

Solution

f (t) = cos^{4} (t) + sin^{4} (t)

Solution

Period : π

Domain : - \infty < t < \infty

Range : \frac{1}{2} \leq f (t) \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

cos^{4} (t) + sin^{4} (t) : π

Domain of

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

Range of

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

Axis interception points of

cos^{4} (t) + sin^{4} (t) :

Y Intercepts

: (0, 1)

Asymptotes of

cos^{4} (t) + sin^{4} (t) :

None

Extreme Points of

cos^{4} (t) + sin^{4} (t) :

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})

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Frequently Asked Questions (FAQ)

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