zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

sin(4x)>0.5

解答

sin (4 x) > 0.5

解答

\frac{π}{24} + \frac{π}{2} n < x < \frac{5 π}{24} + \frac{π}{2} n

+2

间隔符号

(\frac{π}{24} + \frac{π}{2} n, \frac{5 π}{24} + \frac{π}{2} n)

十进制

0.13089 \dots + \frac{π}{2} n < x < 0.65449 \dots + \frac{π}{2} n

求解步骤

sin (4 x) > 0.5

对于

sin (x) > a

，若

- 1 \leq a < 1

，则

arcsin (a) + 2 πn < x < π - arcsin (a) + 2 πn

arcsin (0.5) + 2 πn < 4 x < π - arcsin (0.5) + 2 πn

若

a < u < b

，则

a < u and u < b

arcsin (0.5) + 2 πn < 4 x and 4 x < π - arcsin (0.5) + 2 πn

arcsin (0.5) + 2 πn < 4 x : x > \frac{π}{24} + \frac{πn}{2}

arcsin (0.5) + 2 πn < 4 x

交换两边

4 x > arcsin (0.5) + 2 πn

化简

arcsin (0.5) + 2 πn : \frac{π}{6} + 2 πn

arcsin (0.5) + 2 πn

arcsin (0.5) = \frac{π}{6}

arcsin (0.5)

= 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{π}{6} + 2 πn

4 x > \frac{π}{6} + 2 πn

两边除以

4

4 x > \frac{π}{6} + 2 πn

两边除以

4

\frac{4 x}{4} > \frac{\frac{π}{6}}{4} + \frac{2 πn}{4}

化简

\frac{4 x}{4} > \frac{\frac{π}{6}}{4} + \frac{2 πn}{4}

化简

\frac{4 x}{4} : x

\frac{4 x}{4}

数字相除:

\frac{4}{4} = 1

= x

化简

\frac{\frac{π}{6}}{4} + \frac{2 πn}{4} : \frac{π}{24} + \frac{πn}{2}

\frac{\frac{π}{6}}{4} + \frac{2 πn}{4}

\frac{\frac{π}{6}}{4} = \frac{π}{24}

\frac{\frac{π}{6}}{4}

使用分式法则:

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

= \frac{π}{6 \cdot 4}

数字相乘:

6 \cdot 4 = 24

= \frac{π}{24}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

约分:

2

= \frac{πn}{2}

= \frac{π}{24} + \frac{πn}{2}

x > \frac{π}{24} + \frac{πn}{2}

x > \frac{π}{24} + \frac{πn}{2}

x > \frac{π}{24} + \frac{πn}{2}

4 x < π - arcsin (0.5) + 2 πn : x < \frac{5 π}{24} + \frac{π}{2} n

4 x < π - arcsin (0.5) + 2 πn

化简

π - arcsin (0.5) + 2 πn : π - \frac{π}{6} + 2 πn

π - arcsin (0.5) + 2 πn

arcsin (0.5) = \frac{π}{6}

arcsin (0.5)

= 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} + 2 πn

4 x < π - \frac{π}{6} + 2 πn

两边除以

4

4 x < π - \frac{π}{6} + 2 πn

两边除以

4

\frac{4 x}{4} < \frac{π}{4} - \frac{\frac{π}{6}}{4} + \frac{2 πn}{4}

化简

\frac{4 x}{4} < \frac{π}{4} - \frac{\frac{π}{6}}{4} + \frac{2 πn}{4}

化简

\frac{4 x}{4} : x

\frac{4 x}{4}

数字相除:

\frac{4}{4} = 1

= x

化简

\frac{π}{4} - \frac{\frac{π}{6}}{4} + \frac{2 πn}{4} : \frac{π}{4} - \frac{π}{24} + \frac{πn}{2}

\frac{π}{4} - \frac{\frac{π}{6}}{4} + \frac{2 πn}{4}

\frac{\frac{π}{6}}{4} = \frac{π}{24}

\frac{\frac{π}{6}}{4}

使用分式法则:

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

= \frac{π}{6 \cdot 4}

数字相乘:

6 \cdot 4 = 24

= \frac{π}{24}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

约分:

2

= \frac{πn}{2}

= \frac{π}{4} - \frac{π}{24} + \frac{πn}{2}

x < \frac{π}{4} - \frac{π}{24} + \frac{πn}{2}

x < \frac{π}{4} - \frac{π}{24} + \frac{πn}{2}

化简

\frac{π}{4} - \frac{π}{24} : \frac{5 π}{24}

\frac{π}{4} - \frac{π}{24}

4, 24

的最小公倍数:

24

4, 24

最小公倍数 (LCM)

4

质因数分解:

2 \cdot 2

4

4

除以

24 = 2 \cdot 2

= 2 \cdot 2

24

质因数分解:

2 \cdot 2 \cdot 2 \cdot 3

24

24

除以

224 = 12 \cdot 2

= 2 \cdot 12

12

除以

212 = 6 \cdot 2

= 2 \cdot 2 \cdot 6

6

除以

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 2 \cdot 2 \cdot 3

将每个因子乘以它在

4

或

24

中出现的最多次数

= 2 \cdot 2 \cdot 2 \cdot 3

数字相乘:

2 \cdot 2 \cdot 2 \cdot 3 = 24

= 24

根据最小公倍数调整分式

将每个分子乘以其分母转变为最小公倍数所要乘以的同一数值

24

对于

\frac{π}{4} :

将分母和分子乘以

6

\frac{π}{4} = \frac{π 6}{4 \cdot 6} = \frac{π 6}{24}

= \frac{π 6}{24} - \frac{π}{24}

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}{24}

同类项相加:

6 π - π = 5 π

= \frac{5 π}{24}

x < \frac{5 π}{24} + \frac{π}{2} n

x < \frac{5 π}{24} + \frac{π}{2} n

合并区间

x > \frac{π}{24} + \frac{πn}{2} and x < \frac{5 π}{24} + \frac{π}{2} n

合并重叠的区间

\frac{π}{24} + \frac{π}{2} n < x < \frac{5 π}{24} + \frac{π}{2} n

流行的例子

sin (18 0^{\circ} - x) < 0

2sin(2x-30)+1>0

2 sin (2 x - 30) + 1 > 0

cos (x) < - \frac{1}{2}

tan^2(x)-3tan(x)+2<0

tan^{2} (x) - 3 tan (x) + 2 < 0

solvefor x,arctan(|x-y|)>0

so l v e f or x, arctan (∣ x - y ∣) > 0