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受欢迎的三角函数 >

sin(x)-2<=-5/2

解答

sin (x) - 2 \leq - \frac{5}{2}

解答

- \frac{5 π}{6} + 2 πn \leq x \leq - \frac{π}{6} + 2 πn

+2

间隔符号

[- \frac{5 π}{6} + 2 πn, - \frac{π}{6} + 2 πn]

十进制

- 2.61799 \dots + 2 πn \leq x \leq - 0.52359 \dots + 2 πn

求解步骤

sin (x) - 2 \leq - \frac{5}{2}

将

2

到右边

sin (x) - 2 \leq - \frac{5}{2}

两边加上

2

sin (x) - 2 + 2 \leq - \frac{5}{2} + 2

化简

sin (x) - 2 + 2 \leq - \frac{5}{2} + 2

化简

sin (x) - 2 + 2 : sin (x)

sin (x) - 2 + 2

同类项相加:

- 2 + 2 \leq 0

= sin (x)

化简

- \frac{5}{2} + 2 : - \frac{1}{2}

- \frac{5}{2} + 2

将项转换为分式:

2 = \frac{2 \cdot 2}{2}

= \frac{2 \cdot 2}{2} - \frac{5}{2}

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{2 \cdot 2 - 5}{2}

2 \cdot 2 - 5 = - 1

2 \cdot 2 - 5

数字相乘:

2 \cdot 2 = 4

= 4 - 5

数字相减:

4 - 5 = - 1

= - 1

= \frac{- 1}{2}

使用分式法则:

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

= - \frac{1}{2}

sin (x) \leq - \frac{1}{2}

sin (x) \leq - \frac{1}{2}

sin (x) \leq - \frac{1}{2}

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

化简

- π - arcsin (- \frac{1}{2}) : - \frac{5 π}{6}

- π - arcsin (- \frac{1}{2})

arcsin (- \frac{1}{2}) = - \frac{π}{6}

arcsin (- \frac{1}{2})

利用以下特性:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{1}{2}) = - arcsin (\frac{1}{2})

= - arcsin (\frac{1}{2})

使用以下普通恒等式:

arcsin (\frac{1}{2}) = \frac{π}{6}

arcsin (\frac{1}{2})

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}{6}

= - \frac{π}{6}

= - π - (- \frac{π}{6})

化简

- π - (- \frac{π}{6})

使用法则

- (- a) = a

= - π + \frac{π}{6}

将项转换为分式:

π = \frac{π 6}{6}

= - \frac{π 6}{6} + \frac{π}{6}

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 6 + π}{6}

同类项相加:

- 6 π + π = - 5 π

= \frac{- 5 π}{6}

使用分式法则:

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

= - \frac{5 π}{6}

= - \frac{5 π}{6}

化简

arcsin (- \frac{1}{2}) : - \frac{π}{6}

arcsin (- \frac{1}{2})

利用以下特性:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{1}{2}) = - arcsin (\frac{1}{2})

= - arcsin (\frac{1}{2})

使用以下普通恒等式:

arcsin (\frac{1}{2}) = \frac{π}{6}

arcsin (\frac{1}{2})

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}{6}

= - \frac{π}{6}

- \frac{5 π}{6} + 2 πn \leq x \leq - \frac{π}{6} + 2 πn

流行的例子

tan(1/x)<= tan(1/(x+1))

tan (\frac{1}{x}) \leq tan (\frac{1}{x + 1})

cos(x^4)+sin(x^4)>= 0.5

cos (x^{4}) + sin (x^{4}) \geq 0.5

1 - tan (x) < 2

2 sin (x) - 1 \geq - 3

2sin(x)>sqrt(3)

2 sin (x) > 3