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受欢迎的三角函数 >

2sin(x/2)>1

解答

2 sin (\frac{x}{2}) > 1

解答

\frac{π}{3} + 4 πn < x < \frac{5 π}{3} + 4 πn

+2

间隔符号

(\frac{π}{3} + 4 πn, \frac{5 π}{3} + 4 πn)

十进制

1.04719 \dots + 4 πn < x < 5.23598 \dots + 4 πn

求解步骤

2 sin (\frac{x}{2}) > 1

两边除以

2

2 sin (\frac{x}{2}) > 1

两边除以

2

\frac{2 sin ( \frac{x}{2} )}{2} > \frac{1}{2}

化简

sin (\frac{x}{2}) > \frac{1}{2}

sin (\frac{x}{2}) > \frac{1}{2}

对于

sin (x) > a

，若

- 1 \leq a < 1

，则

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

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

若

a < u < b

，则

a < u and u < b

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

arcsin (\frac{1}{2}) + 2 πn < \frac{x}{2} : x > \frac{π}{3} + 4 πn

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

交换两边

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

化简

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

arcsin (\frac{1}{2}) + 2 πn

使用以下普通恒等式:

arcsin (\frac{1}{2}) = \frac{π}{6}

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} + 2 πn

\frac{x}{2} > \frac{π}{6} + 2 πn

在两边乘以

2

\frac{x}{2} > \frac{π}{6} + 2 πn

在两边乘以

2

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

化简

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

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

2 \cdot \frac{π}{6} + 2 \cdot 2 πn : \frac{π}{3} + 4 πn

2 \cdot \frac{π}{6} + 2 \cdot 2 πn

2 \cdot \frac{π}{6} = \frac{π}{3}

2 \cdot \frac{π}{6}

分式相乘:

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

= \frac{π 2}{6}

约分:

2

= \frac{π}{3}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

数字相乘:

2 \cdot 2 = 4

= 4 πn

= \frac{π}{3} + 4 πn

x > \frac{π}{3} + 4 πn

x > \frac{π}{3} + 4 πn

x > \frac{π}{3} + 4 πn

\frac{x}{2} < π - arcsin (\frac{1}{2}) + 2 πn : x < \frac{5 π}{3} + 4 πn

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

化简

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

π - arcsin (\frac{1}{2}) + 2 πn

使用以下普通恒等式:

arcsin (\frac{1}{2}) = \frac{π}{6}

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}{6} + 2 πn

\frac{x}{2} < π - \frac{π}{6} + 2 πn

在两边乘以

2

\frac{x}{2} < π - \frac{π}{6} + 2 πn

在两边乘以

2

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

化简

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

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

2 π - 2 \cdot \frac{π}{6} + 2 \cdot 2 πn : 2 π - \frac{π}{3} + 4 πn

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

2 \cdot \frac{π}{6} = \frac{π}{3}

2 \cdot \frac{π}{6}

分式相乘:

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

= \frac{π 2}{6}

约分:

2

= \frac{π}{3}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

数字相乘:

2 \cdot 2 = 4

= 4 πn

= 2 π - \frac{π}{3} + 4 πn

x < 2 π - \frac{π}{3} + 4 πn

x < 2 π - \frac{π}{3} + 4 πn

化简

2 π - \frac{π}{3} : \frac{5 π}{3}

2 π - \frac{π}{3}

将项转换为分式:

2 π = \frac{2 π 3}{3}

= \frac{2 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{2 π 3 - π}{3}

2 π 3 - π = 5 π

2 π 3 - π

数字相乘:

2 \cdot 3 = 6

= 6 π - π

同类项相加:

6 π - π = 5 π

= 5 π

= \frac{5 π}{3}

x < \frac{5 π}{3} + 4 πn

x < \frac{5 π}{3} + 4 πn

合并区间

x > \frac{π}{3} + 4 πn and x < \frac{5 π}{3} + 4 πn

合并重叠的区间

\frac{π}{3} + 4 πn < x < \frac{5 π}{3} + 4 πn

流行的例子

8-9sin(x)cos(x)>20

8 - 9 sin (x) cos (x) > 20

cos^2(x)-2cos(x)+1<= 0

cos^{2} (x) - 2 cos (x) + 1 \leq 0

cos (x) sin (x) < 0

2cos^2(x)-cos(x)-1>0

2 cos^{2} (x) - cos (x) - 1 > 0

sqrt(3)tan(x)<1

3 tan (x) < 1