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受欢迎的三角函数 >

sin(x)<= (sqrt(3))/2 ,-pi<= x<= pi

解答

sin (x) \leq \frac{3}{2}, - π \leq x \leq π

解答

- π \leq x \leq \frac{π}{3} or 2 π - \frac{4 π}{3} \leq x \leq π

+2

间隔符号

[- π, \frac{π}{3}] \cup [2 π - \frac{4 π}{3}, π]

十进制

- 3.14159 \dots \leq x \leq 1.04719 \dots or 2.09439 \dots \leq x \leq 3.14159 \dots

求解步骤

sin (x) \leq \frac{3}{2}, - π \leq x \leq π

对于

sin (x) \leq a

，若

- 1 < a < 1

，则

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

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

化简

- π - arcsin (\frac{3}{2}) : - \frac{4 π}{3}

- π - arcsin (\frac{3}{2})

使用以下普通恒等式:

arcsin (\frac{3}{2}) = \frac{π}{3}

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 - \frac{π}{3}

化简

- π - \frac{π}{3}

将项转换为分式:

π = \frac{π 3}{3}

= - \frac{π 3}{3} - \frac{π}{3}

因为分母相等，所以合并分式:

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

= \frac{- π 3 - π}{3}

同类项相加:

- 3 π - π = - 4 π

= \frac{- 4 π}{3}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{4 π}{3}

= - \frac{4 π}{3}

化简

arcsin (\frac{3}{2}) : \frac{π}{3}

arcsin (\frac{3}{2})

使用以下普通恒等式:

arcsin (\frac{3}{2}) = \frac{π}{3}

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}

= \frac{π}{3}

- \frac{4 π}{3} + 2 πn \leq x \leq \frac{π}{3} + 2 πn

合并区间

- \frac{4 π}{3} + 2 πn \leq x \leq \frac{π}{3} + 2 πn and - π \leq x \leq π

- π \leq x \leq \frac{π}{3} or 2 π - \frac{4 π}{3} \leq x \leq π

作图

流行的例子

2cos(4x-pi/3)-1<= 0

2 cos (4 x - \frac{π}{3}) - 1 \leq 0

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arccos((x-5)/(10))-pi/3 >= 0

arccos (\frac{x - 5}{10}) - \frac{π}{3} \geq 0

tan(3x-1)>-sqrt(3)

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sin(x)>= 0,(1-2sin(x))/(1+sin(x))>0

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