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受欢迎的三角函数 >

100=(50)/(sin(x/2))

解答

100 = \frac{50}{sin ( \frac{x}{2} )}

解答

x = \frac{π}{3} + 4 πn, x = \frac{5 π}{3} + 4 πn

+1

度数

x = 6 0^{\circ} + 72 0^{\circ} n, x = 30 0^{\circ} + 72 0^{\circ} n

求解步骤

100 = \frac{50}{sin ( \frac{x}{2} )}

交换两边

\frac{50}{sin ( \frac{x}{2} )} = 100

在两边乘以

sin (\frac{x}{2})

\frac{50}{sin ( \frac{x}{2} )} = 100

在两边乘以

sin (\frac{x}{2})

\frac{50}{sin ( \frac{x}{2} )} sin (\frac{x}{2}) = 100 sin (\frac{x}{2})

化简

50 = 100 sin (\frac{x}{2})

50 = 100 sin (\frac{x}{2})

交换两边

100 sin (\frac{x}{2}) = 50

两边除以

100

100 sin (\frac{x}{2}) = 50

两边除以

100

\frac{100 sin ( \frac{x}{2} )}{100} = \frac{50}{100}

化简

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

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

验证解

找到无定义的点（奇点）:

sin (\frac{x}{2}) = 0

取

\frac{50}{sin ( \frac{x}{2} )}

的分母，令其等于零

sin (\frac{x}{2}) = 0

以下点无定义

sin (\frac{x}{2}) = 0

将不在定义域的点与解相综合:

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

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

的通解

sin (x)

周期表（周期为

2 πn

"）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{x}{2} = \frac{π}{6} + 2 πn, \frac{x}{2} = \frac{5 π}{6} + 2 πn

\frac{x}{2} = \frac{π}{6} + 2 πn, \frac{x}{2} = \frac{5 π}{6} + 2 πn

解

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

解

\frac{x}{2} = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{3} + 4 πn

\frac{x}{2} = \frac{5 π}{6} + 2 πn

在两边乘以

2

\frac{x}{2} = \frac{5 π}{6} + 2 πn

在两边乘以

2

\frac{2 x}{2} = 2 \cdot \frac{5 π}{6} + 2 \cdot 2 πn

化简

\frac{2 x}{2} = 2 \cdot \frac{5 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{5 π}{6} + 2 \cdot 2 πn : \frac{5 π}{3} + 4 πn

2 \cdot \frac{5 π}{6} + 2 \cdot 2 πn

2 \cdot \frac{5 π}{6} = \frac{5 π}{3}

2 \cdot \frac{5 π}{6}

分式相乘:

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

= \frac{5 π 2}{6}

数字相乘:

5 \cdot 2 = 10

= \frac{10 π}{6}

约分:

2

= \frac{5 π}{3}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

数字相乘:

2 \cdot 2 = 4

= 4 πn

= \frac{5 π}{3} + 4 πn

x = \frac{5 π}{3} + 4 πn

x = \frac{5 π}{3} + 4 πn

x = \frac{5 π}{3} + 4 πn

x = \frac{π}{3} + 4 πn, x = \frac{5 π}{3} + 4 πn

作图

流行的例子

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