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Popular >

0<-pisin(pix)

Solution

0 < - π sin (π x)

Solution

- 1 + 2 n < x < 2 n

Interval Notation

(- 1 + 2 n, 2 n)

Solution steps

0 < - π sin (π x)

Switch sides

- π sin (π x) > 0

Multiply both sides by

- 1

- π sin (π x) > 0

Multiply both sides by -1 (reverse the inequality)

(- π sin (π x)) (- 1) < 0 \cdot (- 1)

Simplify

π sin (π x) < 0

π sin (π x) < 0

Divide both sides by

π

π sin (π x) < 0

Divide both sides by

π

\frac{π sin ( π x )}{π} < \frac{0}{π}

Simplify

sin (π x) < 0

sin (π x) < 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 < π x < arcsin (0) + 2 πn

a < u < b

then

a < u and u < b

- π - arcsin (0) + 2 πn < π x and π x < arcsin (0) + 2 πn

- π - arcsin (0) + 2 πn < π x : x > 2 n - 1

- π - arcsin (0) + 2 πn < π x

Switch sides

π x > - π - arcsin (0) + 2 πn

Simplify

- π - arcsin (0) + 2 πn : 2 πn - π

- π - arcsin (0) + 2 πn

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 + 2 πn

- π - 0 + 2 πn = - π + 2 πn

= 2 πn - π

π x > 2 πn - π

Divide both sides by

π

π x > 2 πn - π

Divide both sides by

π

\frac{π x}{π} > \frac{2 πn}{π} - \frac{π}{π}

Simplify

\frac{π x}{π} > \frac{2 πn}{π} - \frac{π}{π}

Simplify

\frac{π x}{π} : x

\frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

\frac{2 πn}{π} - \frac{π}{π} : 2 n - 1

\frac{2 πn}{π} - \frac{π}{π}

Apply rule

\frac{a}{a} = 1

\frac{π}{π} = 1

= \frac{2 πn}{π} - 1

Cancel

\frac{2 πn}{π} : 2 n

\frac{2 πn}{π}

Cancel the common factor:

π

= 2 n

= 2 n - 1

x > 2 n - 1

x > 2 n - 1

x > 2 n - 1

π x < arcsin (0) + 2 πn : x < 2 n

π x < arcsin (0) + 2 πn

Simplify

arcsin (0) + 2 πn : 2 πn

arcsin (0) + 2 πn

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 + 2 πn

0 + 2 πn = 2 πn

= 2 πn

π x < 2 πn

Divide both sides by

π

π x < 2 πn

Divide both sides by

π

\frac{π x}{π} < \frac{2 πn}{π}

Simplify

x < 2 n

x < 2 n

Combine the intervals

x > 2 n - 1 and x < 2 n

Merge Overlapping Intervals

- 1 + 2 n < x < 2 n

Popular Examples

(cos(x)-1)(cos(x)+1/2)>= 0

(cos (x) - 1) (cos (x) + \frac{1}{2}) \geq 0

tan(x)< pi/2

tan (x) < \frac{π}{2}

cos(x-1)>= 0

cos (x - 1) \geq 0

sin(θ)<0,sec(θ)>0

sin (θ) < 0, sec (θ) > 0

-pi/(12)sin^2(pi/(12)t)<0

- \frac{π}{12} sin^{2} (\frac{π}{12} t) < 0