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受欢迎的三角函数 >

sin((5x)/2)<= 0.6

解答

sin (\frac{5 x}{2}) \leq 0.6

解答

- 1.51403 \dots + \frac{4 π}{5} n \leq x \leq 0.25740 \dots + \frac{4 π}{5} n

+1

间隔符号

[- 1.51403 \dots + \frac{4 π}{5} n, 0.25740 \dots + \frac{4 π}{5} n]

求解步骤

sin (\frac{5 x}{2}) \leq 0.6

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 (0.6) + 2 πn \leq \frac{5 x}{2} \leq arcsin (0.6) + 2 πn

若

a \leq u \leq b

，则

a \leq u and u \leq b

- π - arcsin (0.6) + 2 πn \leq \frac{5 x}{2} and \frac{5 x}{2} \leq arcsin (0.6) + 2 πn

- π - arcsin (0.6) + 2 πn \leq \frac{5 x}{2} : x \geq \frac{- 2 π - 2 arcsin ( 0.6 )}{5} + \frac{4 π}{5} n

- π - arcsin (0.6) + 2 πn \leq \frac{5 x}{2}

交换两边

\frac{5 x}{2} \geq - π - arcsin (0.6) + 2 πn

在两边乘以

2

\frac{5 x}{2} \geq - π - arcsin (0.6) + 2 πn

在两边乘以

2

\frac{2 \cdot 5 x}{2} \geq - 2 π - 2 arcsin (0.6) + 2 \cdot 2 πn

化简

5 x \geq - 2 π - 2 arcsin (0.6) + 4 πn

5 x \geq - 2 π - 2 arcsin (0.6) + 4 πn

两边除以

5

5 x \geq - 2 π - 2 arcsin (0.6) + 4 πn

两边除以

5

\frac{5 x}{5} \geq - \frac{2 π}{5} - \frac{2 arcsin ( 0.6 )}{5} + \frac{4 πn}{5}

化简

x \geq - \frac{2 π}{5} - \frac{2 arcsin ( 0.6 )}{5} + \frac{4 πn}{5}

化简

- \frac{2 π}{5} - \frac{2 arcsin ( 0.6 )}{5} : \frac{- 2 π - 2 arcsin ( 0.6 )}{5}

- \frac{2 π}{5} - \frac{2 arcsin ( 0.6 )}{5}

使用法则

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

= \frac{- 2 π - 2 arcsin ( 0.6 )}{5}

x \geq \frac{- 2 π - 2 arcsin ( 0.6 )}{5} + \frac{4 π}{5} n

x \geq \frac{- 2 π - 2 arcsin ( 0.6 )}{5} + \frac{4 π}{5} n

\frac{5 x}{2} \leq arcsin (0.6) + 2 πn : x \leq \frac{2 arcsin ( 0.6 )}{5} + \frac{4 πn}{5}

\frac{5 x}{2} \leq arcsin (0.6) + 2 πn

在两边乘以

2

\frac{5 x}{2} \leq arcsin (0.6) + 2 πn

在两边乘以

2

\frac{2 \cdot 5 x}{2} \leq 2 arcsin (0.6) + 2 \cdot 2 πn

化简

5 x \leq 2 arcsin (0.6) + 4 πn

5 x \leq 2 arcsin (0.6) + 4 πn

两边除以

5

5 x \leq 2 arcsin (0.6) + 4 πn

两边除以

5

\frac{5 x}{5} \leq \frac{2 arcsin ( 0.6 )}{5} + \frac{4 πn}{5}

化简

x \leq \frac{2 arcsin ( 0.6 )}{5} + \frac{4 πn}{5}

x \leq \frac{2 arcsin ( 0.6 )}{5} + \frac{4 πn}{5}

合并区间

x \geq \frac{- 2 π - 2 arcsin ( 0.6 )}{5} + \frac{4 π}{5} n and x \leq \frac{2 arcsin ( 0.6 )}{5} + \frac{4 πn}{5}

合并重叠的区间

- 1.51403 \dots + \frac{4 π}{5} n \leq x \leq 0.25740 \dots + \frac{4 π}{5} n

流行的例子

sqrt(3)-tan(x)<0

3 - tan (x) < 0

cos (\frac{x}{2}) \geq 0

1/2 (10sin(2pi*60x))>-0.52

\frac{1}{2} (10 sin (2 π \cdot 60 x)) > - 0.52

(4cos^2(x)-3)(1-tan^2(x))<= 0

(4 cos^{2} (x) - 3) (1 - tan^{2} (x)) \leq 0

cot(θ)<0,sec(θ)>0

cot (θ) < 0, sec (θ) > 0