it

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popolare Trigonometria >

sin(3x)<= 1/3

Soluzione

sin (3 x) \leq \frac{1}{3}

Soluzione

\frac{- π - arcsin ( \frac{1}{3} )}{3} + \frac{2 π}{3} n \leq x \leq \frac{arcsin ( \frac{1}{3} )}{3} + \frac{2 π}{3} n

+2

Notazione dell’intervallo

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

Decimale

- 1.16047 \dots + \frac{2 π}{3} n \leq x \leq 0.11327 \dots + \frac{2 π}{3} n

Fasi della soluzione

sin (3 x) \leq \frac{1}{3}

Per

sin (x) \leq a

, se

- 1 < a < 1

allora

- π - arcsin (a) + 2 πn \leq x \leq arcsin (a) + 2 πn

- π - arcsin (\frac{1}{3}) + 2 πn \leq 3 x \leq arcsin (\frac{1}{3}) + 2 πn

Se

a \leq u \leq b

allora

a \leq u and u \leq b

- π - arcsin (\frac{1}{3}) + 2 πn \leq 3 x and 3 x \leq arcsin (\frac{1}{3}) + 2 πn

- π - arcsin (\frac{1}{3}) + 2 πn \leq 3 x : x \geq \frac{- π - arcsin ( \frac{1}{3} )}{3} + \frac{2 π}{3} n

- π - arcsin (\frac{1}{3}) + 2 πn \leq 3 x

Scambia i lati

3 x \geq - π - arcsin (\frac{1}{3}) + 2 πn

Dividere entrambi i lati per

3

3 x \geq - π - arcsin (\frac{1}{3}) + 2 πn

Dividere entrambi i lati per

3

\frac{3 x}{3} \geq - \frac{π}{3} - \frac{arcsin ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

Semplificare

x \geq - \frac{π}{3} - \frac{arcsin ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

Semplificare

- \frac{π}{3} - \frac{arcsin ( \frac{1}{3} )}{3} : \frac{- π - arcsin ( \frac{1}{3} )}{3}

- \frac{π}{3} - \frac{arcsin ( \frac{1}{3} )}{3}

Applicare la regola

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- π - arcsin ( \frac{1}{3} )}{3}

x \geq \frac{- π - arcsin ( \frac{1}{3} )}{3} + \frac{2 π}{3} n

x \geq \frac{- π - arcsin ( \frac{1}{3} )}{3} + \frac{2 π}{3} n

3 x \leq arcsin (\frac{1}{3}) + 2 πn : x \leq \frac{arcsin ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

3 x \leq arcsin (\frac{1}{3}) + 2 πn

Dividere entrambi i lati per

3

3 x \leq arcsin (\frac{1}{3}) + 2 πn

Dividere entrambi i lati per

3

\frac{3 x}{3} \leq \frac{arcsin ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

Semplificare

x \leq \frac{arcsin ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

x \leq \frac{arcsin ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

Combina gli intervalli

x \geq \frac{- π - arcsin ( \frac{1}{3} )}{3} + \frac{2 π}{3} n and x \leq \frac{arcsin ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

Unire gli intervalli sovrapposti

\frac{- π - arcsin ( \frac{1}{3} )}{3} + \frac{2 π}{3} n \leq x \leq \frac{arcsin ( \frac{1}{3} )}{3} + \frac{2 π}{3} n

Esempi popolari

tan(t)<-1/(sqrt(3))

tan (t) < - \frac{1}{3}

sin(x)>= 1/2 ,0<= x<= 2pi

sin (x) \geq \frac{1}{2}, 0 \leq x \leq 2 π

2 cos (x) + 2 \geq 2

(2*cos(x)-3)/(sin(x))>= 0

\frac{2 \cdot cos ( x ) - 3}{sin ( x )} \geq 0

cos^{3} (x^{2}) - 3 > 0