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受欢迎的三角函数 >

(37)/(sin(x))=(30)/(sin(30))

解答

\frac{37}{sin ( x )} = \frac{30}{sin ( 3 0 ^{\circ} )}

解答

x = 0.66450 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.66450 \dots + 36 0^{\circ} n

+1

弧度

x = 0.66450 \dots + 2 πn, x = π - 0.66450 \dots + 2 πn

求解步骤

\frac{37}{sin ( x )} = \frac{30}{sin ( 3 0 ^{\circ} )}

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

使用以下普通恒等式:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

sin (x)

周期表（周期为

36 0^{\circ} n

"）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= \frac{1}{2}

\frac{37}{sin ( x )} = \frac{30}{\frac{1}{2}}

使用分式交叉相乘

\frac{37}{sin ( x )} = \frac{30}{\frac{1}{2}}

使用分式交叉相乘: 若

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

则

a \cdot d = b \cdot c

37 \cdot \frac{1}{2} = sin (x) \cdot 30

化简

37 \cdot \frac{1}{2} : \frac{37}{2}

37 \cdot \frac{1}{2}

将项转换为分式:

37 = \frac{37}{1}

= \frac{1}{2} \cdot \frac{37}{1}

分式相乘:

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

= \frac{37 \cdot 1}{1 \cdot 2}

约分:

1

= \frac{37}{2}

\frac{37}{2} = sin (x) \cdot 30

\frac{37}{2} = sin (x) \cdot 30

交换两边

sin (x) \cdot 30 = \frac{37}{2}

两边除以

30

sin (x) \cdot 30 = \frac{37}{2}

两边除以

30

\frac{sin ( x ) \cdot 30}{30} = \frac{\frac{37}{2}}{30}

化简

\frac{sin ( x ) \cdot 30}{30} = \frac{\frac{37}{2}}{30}

化简

\frac{sin ( x ) \cdot 30}{30} : sin (x)

\frac{sin ( x ) \cdot 30}{30}

数字相除:

\frac{30}{30} = 1

= sin (x)

化简

\frac{\frac{37}{2}}{30} : \frac{37}{60}

\frac{\frac{37}{2}}{30}

使用分式法则:

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

= \frac{37}{2 \cdot 30}

数字相乘:

2 \cdot 30 = 60

= \frac{37}{60}

sin (x) = \frac{37}{60}

sin (x) = \frac{37}{60}

sin (x) = \frac{37}{60}

验证解

找到无定义的点（奇点）:

sin (x) = 0

取

\frac{37}{sin ( x )}

的分母，令其等于零

sin (x) = 0

以下点无定义

sin (x) = 0

将不在定义域的点与解相综合:

sin (x) = \frac{37}{60}

使用反三角函数性质

sin (x) = \frac{37}{60}

sin (x) = \frac{37}{60}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x = arcsin (\frac{37}{60}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{37}{60}) + 36 0^{\circ} n

x = arcsin (\frac{37}{60}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{37}{60}) + 36 0^{\circ} n

以小数形式表示解

x = 0.66450 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.66450 \dots + 36 0^{\circ} n

作图

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