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Popular >

-sin(x)>0

Solution

- sin (x) > 0

Solution

- π + 2 πn < x < 2 πn

+2

Interval Notation

(- π + 2 πn, 2 πn)

Decimal Notation

- 3.14159 \dots + 2 πn < x < 2 πn

Solution steps

- sin (x) > 0

Multiply both sides by

- 1

- sin (x) > 0

Multiply both sides by -1 (reverse the inequality)

(- sin (x)) (- 1) < 0 \cdot (- 1)

Simplify

sin (x) < 0

sin (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 < x < 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 < x < 0 + 2 πn

Simplify

- π + 2 πn < x < 2 πn

Popular Examples

arctan (x) \leq 1

(2sin(x)+1)/(2cos(x))<= 0

\frac{2 sin ( x ) + 1}{2 cos ( x )} \leq 0

sec (x) > 0

sec^{2} (x) \leq 2

2 cos (x) < 1