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Popular >

f(t)=sqrt(9sin^2(4t)-1)

Solution

f (t) = 9 sin^{2} (4 t) - 1

Solution

Domain : \frac{arcsin ( \frac{1}{3} )}{4} + \frac{π}{2} n \leq t \leq \frac{π - arcsin ( \frac{1}{3} )}{4} + \frac{π}{2} n or \frac{- π + arcsin ( \frac{1}{3} )}{4} + \frac{π}{2} n \leq t \leq - \frac{arcsin ( \frac{1}{3} )}{4} + \frac{π}{2} n

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

Asymptotes : None

Extreme Points : Minimum (\frac{arcsin ( \frac{1}{3} )}{4}, 0), Saddle (\frac{π}{8} + \frac{πn}{2}, 9 sin^{2} (4 (\frac{π}{8} + \frac{πn}{2})) - 1), Maximum (\frac{π - arcsin ( \frac{1}{3} )}{4}, 0), Minimum (\frac{- π + arcsin ( \frac{1}{3} )}{4} + \frac{π}{2}, 0), Maximum (\frac{3 π}{8} + \frac{πn}{2}, 9 sin^{2} (4 (\frac{3 π}{8} + \frac{πn}{2})) - 1), Minimum (- \frac{arcsin ( \frac{1}{3} )}{4} + \frac{π}{2}, 0)

+1

Interval Notation

Domain : [\frac{arcsin ( \frac{1}{3} )}{4} + \frac{π}{2} n, \frac{π - arcsin ( \frac{1}{3} )}{4} + \frac{π}{2} n] \cup [\frac{- π + arcsin ( \frac{1}{3} )}{4} + \frac{π}{2} n, - \frac{arcsin ( \frac{1}{3} )}{4} + \frac{π}{2} n]

Solution steps

Domain of

9 sin^{2} (4 t) - 1 : \frac{arcsin ( \frac{1}{3} )}{4} + \frac{π}{2} n \leq t \leq \frac{π - arcsin ( \frac{1}{3} )}{4} + \frac{π}{2} n or \frac{- π + arcsin ( \frac{1}{3} )}{4} + \frac{π}{2} n \leq t \leq - \frac{arcsin ( \frac{1}{3} )}{4} + \frac{π}{2} n

Axis interception points of

9 sin^{2} (4 t) - 1 :

X Intercepts

: (\frac{arcsin ( \frac{1}{3} )}{4} + \frac{πn}{2}, 0), (\frac{π}{4} - \frac{arcsin ( \frac{1}{3} )}{4} + \frac{πn}{2}, 0), (- \frac{arcsin ( \frac{1}{3} )}{4} + \frac{πn}{2}, 0), (\frac{π}{4} + \frac{arcsin ( \frac{1}{3} )}{4} + \frac{πn}{2}, 0)

Asymptotes of

9 sin^{2} (4 t) - 1 :

None

Extreme Points of

9 sin^{2} (4 t) - 1 :

Minimum

(\frac{arcsin ( \frac{1}{3} )}{4}, 0),

Saddle

(\frac{π}{8} + \frac{πn}{2}, 9 sin^{2} (4 (\frac{π}{8} + \frac{πn}{2})) - 1),

Maximum

(\frac{π - arcsin ( \frac{1}{3} )}{4}, 0),

Minimum

(\frac{- π + arcsin ( \frac{1}{3} )}{4} + \frac{π}{2}, 0),

Maximum

(\frac{3 π}{8} + \frac{πn}{2}, 9 sin^{2} (4 (\frac{3 π}{8} + \frac{πn}{2})) - 1),

Minimum

(- \frac{arcsin ( \frac{1}{3} )}{4} + \frac{π}{2}, 0)

Popular Examples

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f (x) = 2 \cdot 2 - 4 x

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f(x)=(3x)/2-1/3

f (x) = \frac{3 x}{2} - \frac{1}{3}

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