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Popular >

8sin^3(t)<0

Solution

8 sin^{3} (t) < 0

Solution

- π + 2 πn < t < 2 πn

+2

Interval Notation

(- π + 2 πn, 2 πn)

Decimal Notation

- 3.14159 \dots + 2 πn < t < 2 πn

Solution steps

8 sin^{3} (t) < 0

Divide both sides by

8

8 sin^{3} (t) < 0

Divide both sides by

8

\frac{8 sin ^{3} ( t )}{8} < \frac{0}{8}

Simplify

sin^{3} (t) < 0

sin^{3} (t) < 0

For

u^{n} < 0

, if

n

is odd then

u < 0

sin (t) < 0

For

sin (x) < a

, if

- 1 < a \leq 1

then

- π - arcsin (a) + 2 πn < x < arcsin (a) + 2 πn

- π - arcsin (0) + 2 πn < t < arcsin (0) + 2 πn

Simplify

- π - arcsin (0) : - π

- π - arcsin (0)

Use the following trivial identity:

arcsin (0) = 0

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= - π - 0

- π - 0 = - π

= - π

Simplify

arcsin (0) : 0

arcsin (0)

Use the following trivial identity:

arcsin (0) = 0

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= 0

- π + 2 πn < t < 0 + 2 πn

Simplify

- π + 2 πn < t < 2 πn

Popular Examples

pi/2-arctan(e^x)>0.1

\frac{π}{2} - arctan (e^{x}) > 0.1

arctan (\frac{x}{y}) > 0

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cos^{2} (x) - sin^{2} (x) > 0

cos^2(x)>sin^2(x)

cos^{2} (x) > sin^{2} (x)

sec (2 x) < 0