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Popular >

y=sin^4(2t)-cos^4(2t)

Solution

y = sin^{4} (2 t) - cos^{4} (2 t)

Solution

Period : π

Domain : - \infty < t < \infty

Range : - 1 \leq f (t) \leq 1

X Intercepts : (\frac{π}{8} + πn, 0), (\frac{5 π}{8} + πn, 0), (\frac{3 π}{8} + πn, 0), (\frac{7 π}{8} + πn, 0), Y Intercepts : (0, - 1)

Asymptotes : None

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

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 1, 1]

Solution steps

Periodicity of

sin^{4} (2 t) - cos^{4} (2 t) : π

Domain of

sin^{4} (2 t) - cos^{4} (2 t) : - \infty < t < \infty

Range of

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

Axis interception points of

sin^{4} (2 t) - cos^{4} (2 t) :

X Intercepts

: (\frac{π}{8} + πn, 0), (\frac{5 π}{8} + πn, 0), (\frac{3 π}{8} + πn, 0), (\frac{7 π}{8} + πn, 0),

Y Intercepts

: (0, - 1)

Asymptotes of

sin^{4} (2 t) - cos^{4} (2 t) :

None

Extreme Points of

sin^{4} (2 t) - cos^{4} (2 t) :

Minimum

(πn, - 1),

Maximum

(\frac{π}{4} + πn, 1),

Minimum

(\frac{π}{2} + πn, - 1),

Maximum

(\frac{3 π}{4} + πn, 1)

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Frequently Asked Questions (FAQ)

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